91Ó°ÊÓ

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

Use a calculator to evaluate \(f(x)=\log x\) at the indicated value of \(x .\) Round your result to three decimal places. \(x=12.5\)

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.) $$\log _{6} \sqrt[3]{6}$$

Using the One-to-One Property In Exercises \(23-26\) use the One-to-One Property to solve the equation for \(x .\) $$2^{x-3}=16$$

Use a calculator to evaluate \(f(x)=\log x\) at the indicated value of \(x .\) Round your result to three decimal places. \(x=96.75\)

Solve the exponential equation algebraically. Approximate the result to three decimal places. \(4^{-3 t}=0.10\)

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.) $$\log _{4} 16^{2}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. \(2^{3-x}=565\)

Use the properties of logarithms to simplify the expression. \(\log _{11} 11^{7}\)

Using the One-to-One Property In Exercises \(23-26\) use the One-to-One Property to solve the equation for \(x .\) $$5^{x-2}=\frac{1}{125}$$