91Ó°ÊÓ

Write each equation in its equivalent exponential form. $$4=\log _{2} 16$$

The exponential growth model \(A=203 e^{0.011}\) describes the population of the United States, \(A,\) in millions, \(t\) years after \(1970 . What was the population of the United States in \)1970 ?$

Approximate each number using a calculator. Round your answer to three decimal places. \(2^{3.4}\)

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. $$10^{x}=3.91$$

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. $$ \log _{5}(7 \cdot 3) $$

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. $$10^{x}=8.07$$

Approximate each number using a calculator. Round your answer to three decimal places. \(3^{2.4}\)

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. $$ \log _{8}(13 \cdot 7) $$

Write each equation in its equivalent exponential form. $$6=\log _{2} 64$$

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. $$e^{x}=5.7$$