91Ó°ÊÓ

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. $$ \log _{b}\left(\frac{x^{3} y}{z^{2}}\right) $$

Begin by graphing \(f(x)=2^{x} .\) Then use transformations of this graph and a table of coordinates to graph the given function. If applicable, use a graphing utility to confirm your hand-drawn graphs. \(g(x)=2^{x}+2\)

The logistic growth function $$P(x)=\frac{90}{1+271 e^{-0.122 x}}$$ models the percentage, \(P(x),\) of Americans who are \(x\) years old with some coronary heart disease. What percentage of 80 -year-olds have some coronary heart disease?

Solve each logarithmic equation in Exercises \(27-44 .\) Be sure to reject any value of \(x\) that produces the logarithm of a negative number or the logarithm of \(0 .\) $$\log _{5} x=3$$

The logistic growth function $$P(x)=\frac{90}{1+271 e^{-0.122 x}}$$ models the percentage, \(P(x),\) of Americans who are \(x\) years old with some coronary heart disease. At what age is the percentage of some coronary heart -disease \(50 \% ?\)

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. $$ \log \sqrt{100 x} $$

Begin by graphing \(f(x)=2^{x} .\) Then use transformations of this graph and a table of coordinates to graph the given function. If applicable, use a graphing utility to confirm your hand-drawn graphs. \(h(x)=2^{x+1}-1\)

Evaluate each expression without using a calculator. $$\log _{64} 8$$

Solve each logarithmic equation in Exercises \(27-44 .\) Be sure to reject any value of \(x\) that produces the logarithm of a negative number or the logarithm of \(0 .\) $$\log _{4}(x+5)=3$$

Evaluate each expression without using a calculator. $$\log _{81} 9$$