Chapter 4

The exponential models describe the population of the indicated country, \(A,\) in millions, \(t\) years after \(2010 .\) Use these models to solve Exercises \(1-6\) Indis \(\quad A=1173.1 e^{0.005 t}\) Ing \(\quad A=31.5 e^{0.018}\) Japer \(\quad A=127.3 e^{-0.006 t}\) Restis \(\quad A=141.9 e^{-0.005 t}\) What was the population of Japan in \(2010 ?\)

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

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

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ 2^{3.4} $$

Solve each exponential equation in Exercises \(1-22\) by expressing each side as a power of the same base and then equating exponents. $$ 3^{x}-81 $$

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. $$ \log _{7}(7 x) $$

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

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ 3^{2.4} $$

The exponential models describe the population of the indicated country, \(A,\) in millions, \(t\) years after \(2010 .\) Use these models to solve Exercises \(1-6\) Indis \(\quad A=1173.1 e^{0.005 t}\) Ing \(\quad A=31.5 e^{0.018}\) Japer \(\quad A=127.3 e^{-0.006 t}\) Restis \(\quad A=141.9 e^{-0.005 t}\) Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?

Write each equation in its equivalent exponential form. $$ 2=\log _{3} x $$

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ 3^{\sqrt{5}} $$

The exponential models describe the population of the indicated country, \(A,\) in millions, \(t\) years after \(2010 .\) Use these models to solve Exercises \(1-6\) Indis \(\quad A=1173.1 e^{0.005 t}\) Ing \(\quad A=31.5 e^{0.018}\) Japer \(\quad A=127.3 e^{-0.006 t}\) Restis \(\quad A=141.9 e^{-0.005 t}\) Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year?

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. $$ \log _{y}(9 x) $$

Write each equation in its equivalent exponential form. $$ 2=\log _{9} x $$

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ 5^{\sqrt{3}} $$

The exponential models describe the population of the indicated country, \(A,\) in millions, \(t\) years after \(2010 .\) Use these models to solve Exercises \(1-6\) Indis \(\quad A=1173.1 e^{0.005 t}\) Ing \(\quad A=31.5 e^{0.018}\) Japer \(\quad A=127.3 e^{-0.006 t}\) Restis \(\quad A=141.9 e^{-0.005 t}\) When will India's population be 1377 million?

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. $$ \log (1000 x) $$

Write each equation in its equivalent exponential form. $$ 5=\log _{b} 32 $$

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ 4^{-1.5} $$

The exponential models describe the population of the indicated country, \(A,\) in millions, \(t\) years after \(2010 .\) Use these models to solve Exercises \(1-6\) Indis \(\quad A=1173.1 e^{0.005 t}\) Ing \(\quad A=31.5 e^{0.018}\) Japer \(\quad A=127.3 e^{-0.006 t}\) Restis \(\quad A=141.9 e^{-0.005 t}\) When will India's population be 1491 million?

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. $$ \log (10,000 x) $$

Write each equation in its equivalent exponential form. $$ 3=\log _{b} 27 $$

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ 6^{-1.2} $$

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. $$ \log _{7}\left(\frac{7}{x}\right) $$

Write each equation in its equivalent exponential form. $$ \log _{6} 216=y $$

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ e^{23} $$

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

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

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ e^{3.4} $$

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

Write each equation in its equivalent logarithmic form. $$ 2^{3}=8 $$

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ e^{-0.95} $$

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. $$ \log \left(\frac{x}{1000}\right) $$

Write each equation in its equivalent logarithmic form. $$ 5^{4}=625 $$

In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ e^{-0.75} $$

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. $$ \log _{4}\left(\frac{64}{y}\right) $$

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

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. $$ 5^{-3}=\frac{1}{125} $$

In Exercises \(11-18\), 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. $$ \ln \left(\frac{e^{2}}{5}\right) $$

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

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. $$ \ln \left(\frac{e^{x}}{8}\right) $$

Write each equation in its equivalent logarithmic form. $$ \sqrt[3]{64}=4 $$

In Exercises \(11-18\), graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$ g(x)-\left(\frac{4}{3}\right)^{x} $$

An artifact originally had 16 grams of carbon-l4 present. The decay model \(\bar{A}-16 e^{-9000121}\) describes the amount of carbon- 14 present after \(t\) years. Use this model to solve Exercises \(15-16\). How many grams of carbon-14 will be present in 5715 years?

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. $$ \log _{b} x^{3} $$

Write each equation in its equivalent logarithmic form. $$ 13^{2}=x $$

In Exercises \(11-18\), graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$ h(x)-\left(\frac{1}{2}\right)^{x} $$

An artifact originally had 16 grams of carbon- 14 present. The decay model \(A-16 e^{-9000121}\) describes the amount of carbon- 14 present after \(t\) years Use this model to solve Exercises \(15-16\). How many grams of carbon-14 will be present in \(11,430\) years?