91Ó°ÊÓ

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. $$f(x)=2^{x-1}$$

Using Properties of Logarithms In Exercises \(21-36,\) find the exact value of the logarithmic expression without using a calculator. (If this is not possible, then state the reason.) $$\log _{3} 9$$

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. $$f(x)=4^{x-3}+3$$

Using Properties of Logarithms In Exercises \(21-36,\) find the exact value of the logarithmic expression without using a calculator. (If this is not possible, then state the reason.) $$\log _{5} \frac{1}{125}$$

Use a calculator to evaluate \(f(x)=\log x\) at the indicated value of \(x .\) Round your result to three decimal places. \(x=\frac{1}{500}\)

Solve the exponential equation algebraically. Approximate the result to three decimal places. \(6^{x}+10=47\)

Complete the table assuming continuously compounded interest. $$ \begin{array}{llll} \text { Isotope} & \text { Half-Life } & \text { Initial Quantity } & \text { Amount After } \\ \text { } & \ \text { Years } & \text { } & \text { 1000 Years } \\ \ ^{14}C&\quad5715 & \quad \space 6.5g&\quad \\ \end{array} $$

Using the One-to-One Property In Exercises \(23-26\) use the One-to-One Property to solve the equation for \(x .\) $$3^{x+1}=27$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. \(3^{2 x}=80\)

Complete the table assuming continuously compounded interest. $$ \begin{array}{llll} \text { Isotope} & \text { Half-Life } & \text { Initial Quantity } & \text { Amount After } \\ \text { } & \ \text { Years } & \text { } & \text { 1000 Years } \\ \ ^{14}C&\quad5715 & \quad \space &\quad 2g\\\ \end{array} $$