91Ó°ÊÓ

Approximate each number using a calculator. Round your answer to three decimal places. \(e^{2.3}\)

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. $$5 e^{x}=23$$

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. $$9 e^{x}=107$$

India is currently one of the world's fastest-growing countries. By \(2040,\) the population of India will be larger than the population of China; by 2050 , nearly one-third of the world's population will live in these two countries alone. The exponential growth model \(A=574 e^{0.036 t}\) describes the population of India, \(A,\) in millions, \(t\) years after \(1974 .\) When will India's population be 2732 million?

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

Write each equation in its equivalent exponential form. $$\log _{5} 125=y$$

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. $$ \log _{9}\left(\frac{9}{x}\right) $$

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. $$3 e^{5 x}=1977$$

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. $$ \log \left(\frac{x}{100}\right) $$

Approximate each number using a calculator. Round your answer to three decimal places. \(e^{-0.95}\)