91Ó°ÊÓ

Evaluate each expression without using a calculator. $$\log _{4} 16$$

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. $$ \log _{b}\left(x^{2} y\right) $$

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. $$ \log _{b}\left(x y^{3}\right) $$

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. $$e^{2 x}-2 e^{x}-3=0$$

Evaluate each expression without using a calculator. $$\log _{7} 49$$

Use the exponential growth model, \(A=A_{0} e^{k t},\) to show that the time it takes a population to triple (to grow from \(A_{0}\) to \(3 A_{0}\) ) is given by \(t=\frac{\ln 3}{k}\)Use the formula \(t=\frac{\ln 2}{k}\) that gives the time for a population

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. $$e^{4 x}+5 e^{2 x}-24=0$$

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

With a growth rate \(k\) to double. Express each answer to the nearest whole year. China is growing at a rate of \(1.1 \%\) per year. How long will it take China to double its population?

Evaluate each expression without using a calculator. $$\log _{2} 64$$