6. Exponential & Logarithmic Functions

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. 3 ln x - (1/3) ln y

Find each value. If applicable, give an approximation to four decimal places. ln 98/13

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. 4 ln (x + 6) - 3 ln x

Find each value. If applicable, give an approximation to four decimal places. ln 27 + ln 943

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log₄ 0.863

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. 3 ln x + 5 ln y - 6 ln z

Find each value. If applicable, give an approximation to four decimal places. ln 98 - ln 13

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