91Ó°ÊÓ

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{8}\left(\frac{64}{\sqrt{x+1}}\right)$$

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$9 e^{x}=99$$

Graph functions \(f\) and \(g\) in the same rectangular coordinate system. Select integers from \(-2\) to 2 , inclusive, for \(x\). Then describe how the graph of g is related to the graph of \(f .\) If applicable, use a graphing utility to confirm your hand-drawn graphs. $$f(x)=2^{x} \quad \text { and } \quad g(x)=2^{x+2}$$

Evaluate each expression without using a calculator. $$\log _{6} \frac{1}{6}$$

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$3 e^{5 x}=1977$$

Graph functions \(f\) and \(g\) in the same rectangular coordinate system. Select integers from \(-2\) to 2 , inclusive, for \(x\). Then describe how the graph of g is related to the graph of \(f .\) If applicable, use a graphing utility to confirm your hand-drawn graphs. $$f(x)=2^{x} \text { and } g(x)=2^{x-2}$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{b}\left(\frac{x^{2} y}{z^{2}}\right)$$

Evaluate each expression without using a calculator. $$\log _{2} \frac{1}{8}$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{b}\left(\frac{x^{3} y}{z^{2}}\right)$$

Evaluate each expression without using a calculator. $$\log _{3} \frac{1}{9}$$