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Magazine Problem 6
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. $$ \log (10,000 x) $$
Problem 6
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?
Problem 6
In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ 6^{-1.2} $$
Problem 7
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. $$ \log _{7}\left(\frac{7}{x}\right) $$
Problem 7
In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ e^{23} $$
Problem 7
Write each equation in its equivalent exponential form. $$ \log _{6} 216=y $$
Problem 8
In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ e^{3.4} $$
Problem 8
Write each equation in its equivalent exponential form. $$ \log _{5} 125=y $$
Problem 8
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. $$ \log _{9}\left(\frac{9}{x}\right) $$
Problem 9
In Exercises \(1-10,\) approximate each number using a calculator. Round your answer to three decimal places. $$ e^{-0.95} $$
