91Ó°ÊÓ

Write each equation in its equivalent logarithmic form. $$2^{-4}=\frac{1}{16}$$

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. \(f(x)=5^{x}\)

In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{5}\left(\frac{125}{y}\right) $$

Write each equation in its equivalent logarithmic form. $$5^{-3}=\frac{1}{125}$$

Solve each exponential equation in Exercises \(1-26\) Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$e^{1-8 x}=7957$$

In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \ln \left(\frac{e^{2}}{5}\right) $$

An artifact originally had 16 grams of carbon- 14 present. The decay model \(A=16 e^{-0.0001211}\) describes the amount of carbonI 4 present, \(A,\) in grams, after \(t\) years. How many grams of carbon-14 will be present after 5715 years?

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. \(g(x)=\left(\frac{3}{2}\right)^{x}\)

Solve each exponential equation in Exercises \(1-26\) Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$e^{5 x-3}-2=10,476$$

Write each equation in its equivalent logarithmic form. $$\sqrt[3]{8}=2$$