91Ó°ÊÓ

approximate each number using a calculator. Round your answer to three decimal places. $$ 4^{-1.5} $$

In Exercises 1–8, write each equation in its equivalent exponential form. $$ 5=\log _{b} 32 $$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$ 2^{2 x-1}=32 $$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log (1000 x) $$

The exponential models describe the population of the indicated country, \(A,\) in millions, t years after \(2010 .\) Use these models to solve Exercises \(1-6\) $$ \begin{aligned} &India \quad A=1173.1 e^{0.008 t}\\\ &Iraq \quad A=31.5 e^{0.019 t}\\\ &Japan \quad A=127.3 e^{-0.006 t}\\\ &Russia \quad A=141.9 e^{-0.005 t} \end{aligned} $$ When will India's population be 1377 million?

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$ 3^{2 x+1}=27 $$

approximate each number using a calculator. Round your answer to three decimal places. $$ 6^{-1.2} $$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log (10,000 x) $$

The exponential models describe the population of the indicated country, \(A,\) in millions, t years after \(2010 .\) Use these models to solve Exercises \(1-6\) $$ \begin{aligned} &India \quad A=1173.1 e^{0.008 t}\\\ &Iraq \quad A=31.5 e^{0.019 t}\\\ &Japan \quad A=127.3 e^{-0.006 t}\\\ &Russia \quad A=141.9 e^{-0.005 t} \end{aligned} $$ When will India's population be 1491 million?

In Exercises 1–8, write each equation in its equivalent exponential form. $$ 3=\log _{b} 27 $$