91Ó°ÊÓ

Let \(f(x)=3 x\) and \(g(x)=4 x .\) Find each function and give its domain. $$ g / f $$

Solve each equation. See Example 2 . $$7^{x^{2}+3 x}=\frac{1}{49}$$

Write each logarithmic equation as an exponential equation. See Example 1. Do not solve. $$ \log _{8} \sqrt[3]{8}=\frac{1}{3} $$

Write logarithm as a sum. Then simplify, if possible. \(\log 100 p q\)

Write each logarithmic equation as an exponential equation. See Example 1. Do not solve. $$ t=\log _{b} T_{1} $$

Write each logarithmic equation as an exponential equation. See Example 1. Do not solve. $$ \log _{m} P=101 $$

Each of the following functions is one-to-one. Find the inverse of each function and express it using \(f^{-1}(x)\) notation. \(f(x)=\frac{x-4}{5}\)

Write logarithm as a difference. Then simplify, if possible. \(\log _{6} \frac{x}{36}\)

Write logarithm as the sum and/or difference of logarithms of a single quantity. Then simplify, if possible. \(\ln \frac{e x y}{z}\)

Evaluate each expression without using a calculator. $$ \ln \sqrt[4]{e^{3}} $$