Condense: 4.) In(4) – 3In(x) 5.) log(7) + 4log(a) – log(5) – 6log(b) 6.) (log;(6) – log;(7) +6log;(m) – 4log;(n)) -

Q: Find the first six terms of the expansion of the function e^x log(1+ y)

A: We have to find the first six terms of the expansion of the function              exlog1 + y Here ,…

Q: 2 Find x so that log10 x = log, 10

A:

Q: Suppose that log, x = 5 and log, y = 4 compute %3| log, Vx²y³

A: Given

Q: Q2 (a) Explain the difference between even and odd Fourier series function.

A: First of, we know about Odd numbers are : 1,3,5,7,….. Even numbers are: 2,4,6,8,…..   =>…

Q: Express the indicated logarithm in terms of ?, ? and ? with the assumptions that log 2 = ?, log 3 =…

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Q: -16 (ii) log,(x– 2)+log,(x) =1 32

A:

Q: 4e3x+3-7=53

A: Hi! You have posted multiple questions. So, we will be solving only the first question as nothing is…

Q: Q5/ Find Fourier series of the Function: f(x) = x if (-n <x< n)

A:

Q: Find the exponential function f(x)=a^x that passes through the point (−3,1/27) and has a y-intercept…

A:

Q: Log 2= 0.301, log 3= 0.477, log 5=0.699 and log 7=0.845 Find:  Log 2.4 Log 6/7

A: (i) log(a/b) = log(a) - log(b) (ii) log(ab) = log(a) + log(b)

Q: log,,3 + log, (4x + 1) = log,o (x +1) +1

A:

Q: i3m (a) Find all z such that log:

A:

Q: 5.-find the exponential Ronction fa)= ab? tha satisfies the condition f(0) = -4 and f(-3) = - 500

A:

Q: ´M` Show that loga N log, M – log, N, where a, M,and N

A:

Q: PROVE that log5 100 = 2(1 + log5 2)

A:

Q: log, 12 log, 11 log, 5 log, 27) 2 2 2 2 A) log, V4620 s". 12 C) log, B) log, (12 - s' . 11') D) log,…

A:

Q: (3) Find the domain of f(x) = log(6 + x – x²) (A) (-∞, 3) (B) (-2, 3) (C) (3, ∞) (D) (-∞, -2) U (3,…

A:

Q: f (x) = In(x + 4) + 3 %3D f(2) 3 e2-6- 4 %3D f (x) = log(a- 2) - 8 %3D f (x) = 108+2 ----- f (x) =…

A: Some functions are given and the inverse of the functions are also given. We have to check that…

Q: 7. If log,w= and log; x+logs y=1 , then what is the value of 13 w3D 7 log, +log, 36x y ?

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Q: 11) 2 log(2)-4log(b)

A:

Q: Show that log,(n) € O(log,(n)) for any b>0 with b 1· Generalize this result.

A:

Q: 7. If log, w = and log6x + log6 y = 1, then determine the value of log7 (4) + log6 (36x²y²) ?|

A: topic- logarithmic equations logaa=1log(ab)=log(a)+log(b)logab=log(a)=log(b)log(am)=mlog(a)

Q: (-1,}). Find a formula for the exponential function passing through the points and (1,20) f(z) =…

A:

Q: 10. Prove that (log2 3)-1+ (log4 3)-1 < 2.

A: Simplify the powers of the term (log23)-1+(log43)-1 by writing the terms as fractions.…

Q: Log 2 = 0.301, log 3 = 0.477,  log 5 = 0.699 and log 7 = 0.845 Using this information only, find:-…

A: According to the given information, The given log values are:

Q: D.  Express as a single log and natural log :                ( log3 3 +   log3 6 +  log 3 2 ) – (…

A: Consider the given expression: log33+log36+log32-log318 Here, the objective is to express as a…

Q: Prove that log(x + y) = log(x) + log(y) if, and only if, y = 1, where x > 1.

A:

Q: 2. In (x + 2) + In 2 = 3 | 4. log:9 – logs (x+ 10) = 1 6. log, (x² +3x) – log, (x + 5) = 1

A:

Q: 9.5. Show that (a). Log(1+ i)? = 2L0((1 + i) but (b). Log(-1+i)² + 2Log(-1+ i). %3D

A:

Q: 10. Express 17* as a power with a base of 2. log2 log 17 b. 2 4 log 17 log2 d. 2 a. log, 17* c. log,…

A: As we know from the logarithmic property; logaxb=b·logax, where x,a&gt;0 &amp; a≠1   Let, 174=2x…

Q: x-1 X-n x+n If y = x log show that y, =(- 1)" - 2 (n – 2) ! %3D x+1 (x - 1)" (x + 1)"

A:

Q: . Find the exponential functions of the form f(x) = ab* that pass through 1) (-2, 32) and (1, –)

A: An exponential function is in the general form f(x) = abx We know the points (-2,32) and (1,1/2) ,…

Q: Find the exponential function f(x)=a^x that passes through the point (3,343) and has a y-intercept…

A: We have to find the exponential function f(x)=a^x that passes through the point (3,343) and has a…

Q: 27a b² Evaluate log, (- V81cd whenever log, (a) = 4, log3 (b) = 0, log, (c) = -1, and %| log3 (d) =…

A:

Q: 13. Determine whether or not each statement is true or false for all x>0 & y>0; if a false, provide…

A: The solution is :

Q: 13. Determine whether or not each statement is true or false for all x>0 & y> 0; If a statement is…

A:

Q: 37. Express log b = 16x²vz* in expanded form. %3D V(x-13 A. Log b16 log bx²y log bz-log b (x-1)² B.…

A: We have to apply logarithmic formula

Q: log, x + log, y+ 6log, -

A: Using Rule's of Logarithm

Q: x- log, (x – 6) = log , 9 4) log, (x– 10) + log, 4 = 3 %3D g7 g, (x + 3) – log, x = 1 6) log, 8 +…

A:

Q: 7. Use log, 2 0.4307 and log, 3 0.6826 to approximate the value of log, 12. O A. 1.5440 O B. 0.8681…

A:

Q: A population of bacteria, B, can be modeled using the exponential function B (x) = 3 (2)" , where a…

A:

Q: log, = 3 log, 2– log. (x- 2z) 2 express x in terms of z.

A: Given, logzxz2=3logz2-logzx-2z We have to express x in terms of z.

Q: 2. Which of the following is equivalent to the expression: 2+3 log2 (x + 1) – log (2x – 1)? 2(x+ 1)3…

A: The given expression is: 2+3log2(x+1)-log2(2x-1)

Q: Without using log tables prove that 1orsid ei boeu ss to 16 +12 log10 15 25 +7 log10 24 81 = 1 80…

A:

Q: b) Given that log, (y-1)+log,|| |= z and log, (y+1)+log, x = z-1, Show that y? =1+8² and find the…

A:

Q: Show that 2 + 11n² log,(n³) – 7 = 0(n³)

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Q: Find of, af , for f(x, y) = log₂ (3г² - +y)

A: Solution of given question is written in below steps.

Q: Which is NOT equivalent to logs A. 4 log5 y - log5 3x B. 4 log5 y – log5 3 + log5 x C. 4 log5 y –…

A: We can use properties of log to slove the given problem. We have : log a/b = log a - log b And  logx…

Q: 3-Given that a=log, 3 and b=log ,6, find log, 24 in terms of and b

A: