91Ó°ÊÓ

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{4}\left(\frac{\sqrt{x}}{64}\right)$$

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

Evaluate each expression without using a calculator. $$\log _{3} 27$$

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. $$19^{x}=143$$

Graph each function by making a table of coordinates. If applicable, use a graphing unility to confirm your hand-drawn graph. $$f(x)=(0.8)^{x}$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{5}\left(\frac{\sqrt{x}}{25}\right)$$

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. $$5 e^{x}=25$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{6}\left(\frac{36}{\sqrt{x+1}}\right)$$

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. $$f(x)=2^{x} \text { and } g(x)=2^{x+1}$$

Evaluate each expression without using a calculator. $$\log _{5} \frac{1}{5}$$