91Ó°ÊÓ

In Exercises 1–8, write each equation in its equivalent exponential form. $$ 2=\log _{3} x $$

The exponential models describe the population of the indicated country, \(A,\) in millions, t years after \(2010 .\) Use these models to solve Exercises \(1-6\) $$ \begin{aligned} &India \quad A=1173.1 e^{0.008 t}\\\ &Iraq \quad A=31.5 e^{0.019 t}\\\ &Japan \quad A=127.3 e^{-0.006 t}\\\ &Russia \quad A=141.9 e^{-0.005 t} \end{aligned} $$ Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?

approximate each number using a calculator. Round your answer to three decimal places. $$ 3^{\sqrt{5}} $$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$ 5^{x}=125 $$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{7}(7 x) $$

In Exercises 1–8, write each equation in its equivalent exponential form. $$ 2=\log _{9} x $$

The exponential models describe the population of the indicated country, \(A,\) in millions, t years after \(2010 .\) Use these models to solve Exercises \(1-6\) $$ \begin{aligned} &India \quad A=1173.1 e^{0.008 t}\\\ &Iraq \quad A=31.5 e^{0.019 t}\\\ &Japan \quad A=127.3 e^{-0.006 t}\\\ &Russia \quad A=141.9 e^{-0.005 t} \end{aligned} $$ Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year?

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{9}(9 x) $$

approximate each number using a calculator. Round your answer to three decimal places. $$ 5^{\sqrt{3}} $$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$ 5^{x}=625 $$