6. Exponential & Logarithmic Functions

Find each value. If applicable, give an approximation to four decimal places. ln 84 - ln 17

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. (1/2)(log x + log y)

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. $\frac{1}{2} \left( \log_5 x + \log_5 y \right) - 2 \log_5 (x + 1)$

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. $\frac{1}{3} \left[ 2 \ln(x + 5) - \ln x - \ln (x^2 - 4) \right]$

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. log_0.1 17

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log_π 63

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log₂ 5

Use a graphing utility and the change-of-base property to graph each function. y = log₃ x

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. log₈ 0.59

Expand: $lo{g}_8\left(\frac{4\surd x}{64y3}\right)$

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