91Ó°ÊÓ

Fill in the blanks. \(\log _{x} 81=4\) is _____ to \(x^{4}=81.\)

Fill in the blanks. When reading the notation \(f(g(x)),\) we say "f _____ g _____ x ".

Determine whether each of the following functions model exponential growth or exponential decay. a. \(D(t)=150(0.44)^{t}\) b. \(H(t)=15,000(1.03)^{t}\)

Fill in the blanks. a. Find \(\frac{\log 8}{\log 5} .\) Round to four decimal places. b. Find \(\frac{3 \ln 12}{\ln 4-\ln 2} .\) Round to four decimal places.

Solve each equation. $$ 6^{x-2}=36 $$

Graph each function. $$ f(x)=e^{x}-2 $$

Solve each equation. Give the exact solution and an approximation to four decimal places. $$ 4^{x}=5 $$

Use a graphing calculator to graph each function. Determine whether the function is an increasing or a decreasing function. See Using Your Calculator: Graphing Exponential Functions. $$ f(x)=-3\left(2^{x / 3}\right) $$

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

Evaluate each expression without using a calculator. $$ \ln e^{5} $$