Determine the numerical value of the following expression without the use of a calculator: + log, (/2 - 2* sin 2-24 + log, (log (915) ++(-1)" + 1) (-1)* + (–1)27 (-1)*60 28 2/2 766

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2. Simplify, in each case state which Logarithmic Law you are using: a. 2log123+ 4log122 b. logg25+ logg10 - 3logg5 c. 4log32-log34-2log3√3-log312 1 riteria 1.1) (Criteria 1.2, 1.3)

Answer the following: 3 (2 + 4i)(-5 + i) [log(7 – 2i)12 - to Exponential Form 1. [(5 < 0.7) + i] + log (-5) i+ i31 + In (4i) - to Exponential Form x = i+ i+i+ i+ vi+ vi+.. 3. ** +}^ +?^ x = ? 2.

Solve for x. log4 (x- 3)= 1-log, (x- 6) If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

1. (1 point) Use properties of logarithms to simplify the following expressions. a.) log.(43)= b.) eIn() = c.) In(e)= d.) log(1) = 2. (1 point) Use properties of logarithms to combine each of the expressions below into one logarithm. a.) log3(x-1)-log3(x+1) b.) log2(x) + log2(y) - log2(z) 3. (1 point) Use properties of logarithms to split each of the expressions below into two logarithms. Remember to simplify all exponents. a.) log(x³y2) b.) In ( 4. (1 point) Consider the logarithmic expression: log,(100) a.) Estimate the value of this expression. b.) Show how to use the change of base formula to rewrite this expression using the common log or the natural log. Then use a calculator to approximate the expression to 2 decimal places.

How do you rewrite the expression 4 logx — 3 log(x^2 + 1) + 2 log(x—1) as a single logarithm log A?