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All Textbook Solutions for Intermediate Algebra

Maria, a biologist is observing the growth pattern of a virus. She starts with 100 of the virus that grows at a rate of 10% per hour. She will check on the virus in 24 hours. How many viruses will she find?In the following exercises, graph each exponential function. 65. f(x)=2x In the following exercises, graph each exponential function. 66. g(x)=3x In the following exercises, graph each exponential function. 67. f(x)=6x In the following exercises, graph each exponential function. 68. g(x)=7x In the following exercises, graph each exponential function. 69. f(x)=(1.5)x In the following exercises, graph each exponential function. 70. g(x)=(2.5)x In the following exercises, graph each exponential function. 71. f(x)=(12)x In the following exercises, graph each exponential function. 72. g(x)=(13)x In the following exercises, graph each exponential function. 73. f(x)=(16)x In the following exercises, graph each exponential function. 74. g(x)=(17)x In the following exercises, graph each exponential function. 75. f(x)=(0.4)x In the following exercises, graph each exponential function. 76. g(x)=(0.6)x In the following exercises, graph each function in the same coordinate system. 77. f(x)=4x,g(x)=4x1 In the following exercises, graph each function in the same coordinate system. 78. f(x)=3x,g(x)=3x1 In the following exercises, graph each function in the same coordinate system. 79. f(x)=2x,g(x)=2x2 In the following exercises, graph each function in the same coordinate system. 80. f(x)=2x,g(x)=2x+2 In the following exercises, graph each function in the same coordinate system. 81. f(x)=3x,g(x)=3x+2 In the following exercises, graph each function in the same coordinate system. 82. f(x)=4x,g(x)=4x+2 In the following exercises, graph each function in the same coordinate system. 83. f(x)=2x,g(x)=2x+1 In the following exercises, graph each function in the same coordinate system. 84. f(x)=2x,g(x)=2x1 In the following exercises, graph each exponential function. 85. f(x)=3x+2 In the following exercises, graph each exponential function. 86. f(x)=3x2 In the following exercises, graph each exponential function. 87. f(x)=2x+3 In the following exercises, graph each exponential function. 88. f(x)=2x3 In the following exercises, graph each exponential function. 89. f(x)=(12)x4 In the following exercises, graph each exponential function. 90. f(x)=(12)x3 In the following exercises, graph each exponential function. 91. f(x)=ex+1 In the following exercises, graph each exponential function. 92. f(x)=ex2 In the following exercises, graph each exponential function. 93 . f(x)=2x In the following exercises, graph each exponential function. 94. f(x)=3x In the following exercises, solve each equation. 95. 23x8=16 In the following exercises, solve each equation. 96. 22x3=32 In the following exercises, solve each equation. 97. 3x+3=9 In the following exercises, solve each equation. 98. 3x2=81 In the following exercises, solve each equation. 99. 4x2=4 In the following exercises, solve each equation. 100. 4x=32 In the following exercises, solve each equation. 101. 4x+2=64 In the following exercises, solve each equation. 102. ä 4x+3=16 In the following exercises, solve each equation. 103.2x2+2x=12 In the following exercises, solve each equation. 104. 3x22x=13 In the following exercises, solve each equation. 105. e3xe4=e10 In the following exercises, solve each equation. 106. e2xe3=e9 In the following exercises, solve each equation. 107. ex2e2=ex In the following exercises, solve each equation. 108. ex2e3=e2x In the following exercises, match the graphs to one of the following functions: 2x 2x+1 2x1 2x+2 2x2 3x In the following exercises, match the graphs to one of the following functions: 2x 2x+1 2x1 2x+2 2x2 3x In the following exercises, match the graphs to one of the following functions: 2x 2x+1 2x1 2x+2 2x2 3x In the following exercises, match the graphs to one of the following functions: 2x 2x+1 2x1 2x+2 2x2 3x In the following exercises, match the graphs to one of the following functions: 2x 2x+1 2x1 2x+2 2x2 3x In the following exercises, match the graphs to one of the following functions: 2x 2x+1 2x1 2x+2 2x2 3x In the following exercises, use an exponential model to solve. 115. Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year, and he does not make any payments for 2 years, how much will he owe on this debt in 2 years by each method of compounding? a. compound quarterly b. compound monthly c. compound continuously In the following exercises, use an exponential model to solve. 116. Cynthia invested $12 000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by each method of compounding? a. compound quarterly b. compound monthly c. compound continuously In the following exercises, use an exponential model to solve. 117. Rochelle deposits $5,000 in an IRA. What will be the value of her investment in 25 years if the investment is earning 8% per year and is compounded continuously?In the following exercises, use an exponential model to solve. 118. Nazerhy deposits $8,000 in a certificate of deposit. The annual interest rate is 6% and the interest will be compounded quarterly. How much will the certificate be worth in 10 years?In the following exercises, use an exponential model to solve. 119. A researcher at the Center for Disease Control and Prevention is studying the growth of a bacteria. He starts his experiment with 100 of the bacteria that grows at a rate of 6% per hour. He will check on the bacteria every 8 hours. How many bacteria will he find in 8 hours?In the following exercises, use an exponential model to solve. 120. A biologist is observing the growth pattern of a virus. She starts with 50 of the virus that grows at a rate of 20% per hour. She will check on the virus in 24 hours. How many viruses will she find?In the following exercises, use an exponential model to solve. 121. In the last ten years the population of Indonesia has grown at a rate of 1.12% per year to 258,316,051. If this rate continues, what will be the population in 10 more years?In the following exercises, use an exponential model to solve. 122. In the last ten years the population of Brazil has grown at a rate of 0.9% per year to 205,823,665. If this rate continues, what will be the population in 10 more years?Explain how you can distinguish between exponential functions and polynomial functions.Compare and contrast the graphs of y=x2 and y=2x.What happens to an exponential function as the values of x decreases? Will the graph ever cross the y -axis? Explain.Convert to logarithmic form: (a) 32=9 (b) 712=7 (c) (13)x=127 Convert to logarithmic form: (a) 43=64 (b) 413=43 (c) (12)x=132 Convert to exponential form: (a) 3=log464 (b) 0=logx1 (c) 2=log101100 Convert to exponential form: (a) 3=log327 (b) 0=logx1 (c) 1=log10110 Find the value of x: (a) logx64=2 (b) log5x=3 (c) log1214=x Find the value of x: (a) logx81=2 (b) log3x=5 (c) log13127=x Find the exact value logarithm without using a calculator: (a)log12144 (b)log42 (c)log2132 Find the exact value logarithm without using a calculator: (a)log981 (b)log82 (c)log319 Graph: y=log3x.Graph: y=log5x.Graph: y=log12x.Graph: y=log14x.Solve: (a) loga121=2 (b) lnx=7 Solve: (a) loga64=3 (b) lnx=9 Solve: (a) log2(5x1)=6 (b) lne3x=6 Solve: (a) log3(4x+3)=3 (b) lne4x=4 What is the decibel level of one of the new quiet dishwashers with intensity 107 watts per square inch?What is the decibel level heavy city traffic with intensity 103 watts per square inch?In 1906, San Francisco experienced an intense earthquake with a magnitude of 7.8 on the Richter scale. In 1989, the Loma Prieta earthquake also affected the San Francisco area, and measured 6.9 on the Richter scale. Compare the intensities of the two earthquakes.In 2014, Chile experienced an intense earthquake with a magnitude of 8.2 on the Richter scale. In 2014, Los Angeles also experienced an earthquake which measured 5.1 on the Richter scale. Compare the intensities of the two earthquakes.In the following exercises, convert form exponential to logarithmic form. 126. 42=16 In the following exercises, convert form exponential to logarithmic form. 127. 25=32 In the following exercises, convert form exponential to logarithmic form. 128. 33=27 In the following exercises, convert form exponential to logarithmic form. 129. 53=125 In the following exercises, convert form exponential to logarithmic form. 130. 103=1000 In the following exercises, convert form exponential to logarithmic form. 131. 102=1100 In the following exercises, convert form exponential to logarithmic form. 132. x12=3 In the following exercises, convert form exponential to logarithmic form. 133. x13=63 In the following exercises, convert form exponential to logarithmic form. 134. 32x=324 In the following exercises, convert form exponential to logarithmic form. 135. 17x=175 In the following exercises, convert form exponential to logarithmic form. 136. (14)2=116 In the following exercises, convert form exponential to logarithmic form. 137. (13)4=181 In the following exercises, convert form exponential to logarithmic form. 138. 32=19 In the following exercises, convert form exponential to logarithmic form. 139. 43=164 In the following exercises, convert form exponential to logarithmic form. 140. ex=6 In the following exercises, convert form exponential to logarithmic form. 141. e3=x In the following exercises, convert each logarithmic equation to exponential form. 142. 3=log464 In the following exercises, convert each logarithmic equation to exponential form. 143. 6=log264 In the following exercises, convert each logarithmic equation to exponential form. 144. 4=logx81 In the following exercises, convert each logarithmic equation to exponential form. 145. 5=logx32 In the following exercises, convert each logarithmic equation to exponential form. 146. 0=log121 In the following exercises, convert each logarithmic equation to exponential form. 147. 0=log71 In the following exercises, convert each logarithmic equation to exponential form. 148. 1=log33 In the following exercises, convert each logarithmic equation to exponential form. 149. 1=log99 In the following exercises, convert each logarithmic equation to exponential form. 150. 4=log10110,000 In the following exercises, convert each logarithmic equation to exponential form. 151. 3=log101,000 In the following exercises, convert each logarithmic equation to exponential form. 152. 5=logex In the following exercises, convert each logarithmic equation to exponential form. 153. x=loge43 In the following exercises, find the value of x in each logarithmic equation. 154. logx49=2 In the following exercises, find the value of x in each logarithmic equation. 155. logx121=2 In the following exercises, find the value of x in each logarithmic equation. 156. logx27=3 In the following exercises, find the value of x in each logarithmic equation. 157. logx64=3 In the following exercises, find the value of x in each logarithmic equation. 158. log3x=4 In the following exercises, find the value of x in each logarithmic equation. 159. log5x=3 In the following exercises, find the value of x in each logarithmic equation. 160. log2x=6 In the following exercises, find the value of x in each logarithmic equation. 161. log3x=5 In the following exercises, find the value of x in each logarithmic equation. 162. log14116=x In the following exercises, find the value of x in each logarithmic equation. 163. log1319=x In the following exercises, find the value of x in each logarithmic equation. 164. log1464=x In the following exercises, find the value of x in each logarithmic equation. 165. log1981=x In the following exercises, find the exact value of each logarithmic without using a calculator. 166. log749 In the following exercises, find the exact value of each logarithmic without using a calculator. 167. log636 In the following exercises, find the exact value of each logarithmic without using a calculator. 168. log41 In the following exercises, find the exact value of each logarithmic without using a calculator. 169. log51 In the following exercises, find the exact value of each logarithmic without using a calculator. 170. log164 In the following exercises, find the exact value of each logarithmic without using a calculator. 171. log273 In the following exercises, find the exact value of each logarithmic without using a calculator. 172. log122 In the following exercises, find the exact value of each logarithmic without using a calculator. 173. log124 In the following exercises, find the exact value of each logarithmic without using a calculator. 174. log2116 In the following exercises, find the exact value of each logarithmic without using a calculator. 175. log3127 In the following exercises, find the exact value of each logarithmic without using a calculator. 176. log4116 In the following exercises, find the exact value of each logarithmic without using a calculator. 177. log9181 In the following exercises, graph each logarithmic function. 178. y=log2x In the following exercises, graph each logarithmic function. 179. y=log4x In the following exercises, graph each logarithmic function. 180. y=log6x In the following exercises, graph each logarithmic function. 181. y=log7x In the following exercises, graph each logarithmic function. 182. y=log1.5x In the following exercises, graph each logarithmic function. 183. y=log2.5x In the following exercises, graph each logarithmic function. 184. y=log13x In the following exercises, graph each logarithmic function. 185. y=log15x In the following exercises, graph each logarithmic function. 186. y=log0.4x In the following exercises, graph each logarithmic function. 187. y=log0.6x In the following exercises, solve each logarithmic equation. 188. loga16=2 In the following exercises, solve each logarithmic equation. 189. loga81=2 In the following exercises, solve each logarithmic equation. 190. loga8=3 In the following exercises, solve each logarithmic equation. 191. ] loga27=3 In the following exercises, solve each logarithmic equation. 192. loga32=2 In the following exercises, solve each logarithmic equation. 193. loga24=3 In the following exercises, solve each logarithmic equation. 194. lnx=5 In the following exercises, solve each logarithmic equation. 195. lnx=4 In the following exercises, solve each logarithmic equation. 196. log2(5x+1)=4 In the following exercises, solve each logarithmic equation. 197. log2(6x+2)=5 In the following exercises, solve each logarithmic equation. 198. log3(4x3)=2 In the following exercises, solve each logarithmic equation. 199. log3(5x4)=4 In the following exercises, solve each logarithmic equation. 200. log4(5x+6)=3 In the following exercises, solve each logarithmic equation. 201. log4(3x2)=2 In the following exercises, solve each logarithmic equation. 202. lne4x=8 In the following exercises, solve each logarithmic equation. 203. lne2x=6 In the following exercises, solve each logarithmic equation. 204. logx2=2 In the following exercises, solve each logarithmic equation. 205. log(x225)=2 In the following exercises, solve each logarithmic equation. 206. log2(x24)=5 In the following exercises, solve each logarithmic equation. 207. log3(x2+2)=3 In the following exercises, use a logarithmic model to solve. 208. What is the decibel level of normal conversation with intensity 106 watts per square inch?In the following exercises, use a logarithmic model to solve. 209. What is the decibel level of a whisper with intensity 1010 watts per square inch?In the following exercises, use a logarithmic model to solve. 210. What is the decibel level of the noise from a motorcycle with intensity 102 watts per square inch?In the following exercises, use a logarithmic model to solve. 211. What is the decibel level of the sound of a garbage disposal with intensity 102 watts per square inch?In the following exercises, use a logarithmic model to solve. 212. In 2014, Chile experienced an intense earthquake with a magnitude of 8.2 on the Richter scale. In 2010, Haiti also experienced an intense earthquake which measured 7.0 on the Richter scale. Compare the intensities of the two earthquakes.In the following exercises, use a logarithmic model to solve. 213. The Los Angeles area experiences many earthquakes. In 1994, the Northridge earthquake measured magnitude of 6.7 on the Richter scale. In 2014, Los Angeles also experienced an earthquake which measured 5.1 on the Richter scale. Compare the intensities of the two earthquakes.In the following exercises, use a logarithmic model to solve. 214. Explain how to change an equation from logarithmic form to exponential form.In the following exercises, use a logarithmic model to solve. 215. Explain the difference between common logarithms and natural logarithms.In the following exercises, use a logarithmic model to solve. 216. Explain why logaax=x.In the following exercises, use a logarithmic model to solve. 217. Explain how to find the log732 on your calculator.Evaluate using the properties of logarithms: (a) log131 (b) log99.Evaluate using the properties of logarithms: (a) log51 (b) log77.Evaluate using the properties of logarithms: (a) 5log515 (b) log774.Evaluate using the properties of logarithms: (a) 2log28 (b) log2215.Use the Product Property of Logarithms to write each logarithm as a sum of logarithms. Simplify, if possible. log33x log28xy Use the Product Property of Logarithms to write each logarithm as a sum of logarithms. Simplify, if possible. log99x log327xy Use the Quotient Property of Logarithms to write each logarithm as a different of logarithms. Simplify, if possible. log434 logx1000 Use the Quotient Property of Logarithms to write each logarithm as a different of logarithms. Simplify, if possible. log254 log10y Use the Power property of Logarithms to write each logarithm as a product of logarithms. Simplify, if possible. log754 logx100 Use the Power property of Logarithms to write each logarithm as a product of logarithms. Simplify, if possible. log237 logx20 Use the Properties of Logarithms to expand the logarithm log2(5x4y2). Simplify, if possible.Use the Properties of Logarithms to expand the logarithm log3(7x5y3). Simplify, if possible.Use the Properties of Logarithms to expand the logarithm logx42y3z25. Simplify, if possible.Use the Properties of Logarithms to expand the logarithm logx25yz3. Simplify, if possible.Use the Properties of Logarithms to condense the logarithm log25+log2xlog2y. Simplify, if possible.Use the Properties of Logarithms to condense the logarithm log36log3xlog3y. Simplify, if possible.Use the Properties of Logarithms to condense the logarithm 3log2x+2log2(x1). Simplify, if possible.Use the Properties of Logarithms to condense the logarithm 2logx+2log(x+1). Simplify, if possible.Rounding to three decimal places, approximate log342.Rounding to three decimal places, approximate log546.In the following exercises, use the properties of logarithms to evaluate. 218. (a) log41 (b) log88 In the following exercises, use the properties of logarithms to evaluate. 219. (a) log121 (b) lne In the following exercises, use the properties of logarithms to evaluate. 220. (a) 3log36 (b) log227 In the following exercises, use the properties of logarithms to evaluate. 221. (a) 5log510 (b) log4410 In the following exercises, use the properties of logarithms to evaluate. 222. (a) 8log87 (b) log662 In the following exercises, use the properties of logarithms to evaluate. 223. (a) 6log615 (b) log884 In the following exercises, use the properties of logarithms to evaluate. 224. (a) 10log5 (b) log102 In the following exercises, use the properties of logarithms to evaluate. 225. (a) 10log3 (b) log101 In the following exercises, use the properties of logarithms to evaluate. 226. (a) eln4 (b) lne2 In the following exercises, use the properties of logarithms to evaluate. 227. (a) eln3 (b) lne7 In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 228. log46x In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 229. log58y In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 230. log232xy In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 231. log381xy In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 232. log100x In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 233. log1000y In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 234. log338 In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 235. log656 In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 236. log416y In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 237. log5125x In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 238. logx10 In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 239. log10,000y In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 240. lne33 In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Simplify if possible. 241. lne416 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 242. log3x2 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 243 log2x5 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 244. logx2 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 245. logx3 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 246. log4x In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 247. log5x3 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 248. lnx3 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 249. lnx43 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 250. log5(4x6y4)In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 251. log2(3x5y3)In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 252. log3(2x2)In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 253. log5(214y3)In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 254. log3xy2z2 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 255. log54ab3c4d2 In the following exercises, use the Properties of Logarithms to expand the logarithm. Simplify if possible. 256. log4x16y4 the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 257. log3x2327y4 In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 258. log22x+y2z2 In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 259. log33x+2y25z2 In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 260. log25x32y2z44 In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 261. log53x24y3z3 In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 262. log64+log69 In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 263. log4+log25 In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 264. log280log25 In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 265. log336log34 In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 266. log34+log3(x+1)In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 267. log25log2(x1)In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 268. log73+log7xlog7y In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 269. log52log5xlog5y In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 270. 4log2x+6log2y In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 271. 6log3x+9log3y In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 272. log3(x21)2log3(x1)In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 273. log(x2+2x+1)2log(x+1)In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 274. 4logx2logy3logz In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 275.3lnx+4lny2lnz In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 276. 13logx3log(x+1)In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible. 277.2log(2x+3)+12log(x+1)In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each other. 278. log342 In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each other. 279. log546 In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each other. 280. log1287 In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each other. 281. log1593 In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each other. 282. log217 In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each other. 283. log321 Write the Product Property in your own words. Does it apply to each of the following? loga5x,loga(5+x). Why or why not?Write the Power Property in your own words. Does it apply to each of the following? logaxp,( logax)r. Why or why not?Use an example to show that log(a+b)loga+logb ?Explain how to find the value of log715 using your calculator.Solve: 2log3x=log336 Solve: 3logx=log64 Solve: log2x+log2(x2)=3 Solve: log2x+log2(x6)=4 Solve: log(x+2)log(4x+3)=logx.Solve: log(x2)log(4x+16)=log1x.Solve 7x=43 . Find the exact answer and then approximate it to three decimal places.Solve 8x=98. Find the exact answer and then approximate it to three decimal places.Solve 2ex2=18 . Find the exact answer and then approximate it to three decimal places.Solve 5e2x=25. Find the exact answer and then approximate it to three decimal places.Hector invests $10,000 at age 21. He hopes the investments will be worth when he turns 50. If the interest compounds continuously, approximately what rate of growth Will he need to achieve his goal?Rachel invests $15,000 at age 25. She hopes the investments will be worth when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal?Researchers recorded that a certain bacteria population grew from 100 to 500 in 6 hours. At this rate of growth, how many bacteria will there be 24 hours from the start of the experiment?Researchers recorded that a certain bacteria population declined from 700,000 to 400,000 in 5 hours after the administration of medication. At this rate of decay, how many bacteria will there be 24 hours from the start of the experiment?The half-life of magnesium-27 is 9.45 minutes. How much of a 10-mg sample will be left in 6 minutes?The half-life of radioactive iodine is 60 days. How much of a 50-mg sample will be left in 40 days?In the following exercises, solve for x. 288. log464=2log4x In the following exercises, solve for x. 289. log49=2logx In the following exercises, solve for x. 290. 3log3x=log327 In the following exercises, solve for x. 291. 3log6x=log664 In the following exercises, solve for x. 292. log5(4x2)=log510 In the following exercises, solve for x. 293. 3 log3(x2+3)=log34x In the following exercises, solve for x. 294. log3x+log3x=2 In the following exercises, solve for x. 295. log4x+log4x=3 In the following exercises, solve for x. 296. log2x+log2(x3)=2 In the following exercises, solve for x. 297. log3x+log3(x+6)=3 In the following exercises, solve for x. 299. logx+log(x15)=2 In the following exercises, solve for x. 299. logx+log(x15)=2 In the following exercises, solve for x. 300. log(x+4)log(5x+12)=logx In the following exercises, solve for x. 301. log(x1)log(x+3)=log1x In the following exercises, solve for x. 302. log5(x+3)+log5(x6)=log510 In the following exercises, solve for x. 303. log5(x+1)+log5(x5)=log57 In the following exercises, solve for x. 304. log3(2x1)=log3(x+3)+log33 In the following exercises, solve for x. 305. log(5x+1)=log(x+3)+log2 In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places. 306. 3x=89 In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places. 307. 2x=74

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