6. Exponential & Logarithmic Functions

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.log x + log(x^2 - 1) - log 7 - log(x + 1)

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log5 13

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log14 87.5

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log0.1 17

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.logπ 63

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_2 5

In Exercises 79–82, use a graphing utility and the change-of-base property to graph each function.y = log3 x

In Exercises 79–82, use a graphing utility and the change-of-base property to graph each function.y = log2 (x + 2)

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_8 0.59

Expand: log8((4√x)/(64y3))

In Exercises 81–100, evaluate or simplify each expression without using a calculator. log 10^7

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. . log_1/2 3

In Exercises 83–88, let logb 2 = A and logb 3 = C and Write each expression in terms of A and C.logb (3/2)

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_π e

In Exercises 83–88, let logb 2 = A and logb 3 = C and Write each expression in terms of A and C.logb 8