91Ó°ÊÓ

Solve each equation. $$ \log _{3}(x-3)=2 $$

Each of the following functions is one-to-one. Find the inverse of each function and express it using \(f^{-1}(x)\) notation. $$ f(x)=\frac{4}{x} $$

Evaluate each expression without using a calculator. $$ \ln e^{6} $$

Computer Viruses. Suppose the number of computers infected by the spread of a virus through an e-mail is described by the exponential function \(c(t)=5(1.034)^{t},\) where \(t\) is the number of minutes since the first infected e-mail was opened. a. Graph the function. Scale the \(t\) -axis from 0 to \(400,\) in units of \(50 .\) Scale the \(c(t)\) -axis from 0 to \(800,000\) in units of \(100,000\) b. Use the function to determine the number of infected computers in 8 hours, which is 480 minutes.

Write each logarithm as the sum and/or difference of logarithms of a single quantity. Then simplify, if possible. See Example 4. $$ \log \frac{7 c}{2} $$

Let \(f(x)=2 x+1\) and \(g(x)=x^{2}-1 .\) Find each of the following. See Example 3 . $$ (g \circ f)(2 x) $$

Evaluate each expression without using a calculator. $$ \ln e^{4} $$

Each of the following functions is one-to-one. Find the inverse of each function and express it using \(f^{-1}(x)\) notation. $$ f(x)=\frac{1}{x} $$

Write each logarithm as the sum and/or difference of logarithms of a single quantity. Then simplify, if possible. See Example 4. $$ \log \frac{9 t}{4} $$

Solve each equation. $$ \log _{4}(2 x-1)=3 $$