91Ó°ÊÓ

Using Properties of Logarithms In Exercises \(15-20\) , use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\log _{5} \frac{1}{250}$$

Graphing an Exponential Function In Exercises \(17-22,\) use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=\left(\frac{1}{2}\right)^{x}$$

Evaluate the function at the indicated value of \(x\) without using a calculator. \(f(x)=\log _{8} x \quad x=1\)

Complete the table for the time \(t\) (in years) necessary for \(P\) dollars to triple when interest is compounded (a) continuously and (b) annually at rate \(r\). \begin{array}{|l|l|l|l|l|l|l|} \hline r & 2 \% & 4 \% & 6 \% & 8 \% & 10 \% & 12 \% \\ \hline t & & & & & & \\ \hline \end{array}

Graphing an Exponential Function In Exercises \(17-22,\) use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=\left(\frac{1}{2}\right)^{-x}$$

Using Properties of Logarithms In Exercises \(15-20\) , use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\log \frac{9}{300}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. \(e^{x^{2}-3}=e^{x-2}\)

Evaluate the function at the indicated value of \(x\) without using a calculator. \(f(x)=\log x \quad x=10\)

Evaluate the function at the indicated value of \(x\) without using a calculator. \(g(x)=\log _{a} x \quad x=a^{2}\)

Graphing an Exponential Function In Exercises \(17-22,\) use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=6^{-x}$$