Exam 9: Logarithmic and Exponential Functions

Use the graph of the piecewise function f(x) to find the following - $(f \circ f)(-3)$

Rewrite in logarithmic form - $e^{x}=3$

Solve. - $\log (x+3)=\log (5 x-1)$

Evaluate. Round to the nearest thousandth, if necessary. - $\ln 0.986$

Express $h(x)$ as a composition of two functions $f(x)$ and $g(x)$ : (f $\circ g)(x)$ . A nsw ers may vary. Choose the possible answer. - $h(x)=8(x+2)^{3}$

Solve the problem. -Approximately one fourth of all glass bottles distributed will be recycled each year. A beverage company distributes 330,000 bottles. The number still in use after $t$ years is given by the function $\mathrm{N}(\mathrm{t})=330,000\left(\frac{1}{4}\right)^{\mathrm{t}}$ After how many years will 4000 bottles still be in use? Round your answer to the nearest tenth.

Use the graph of the piecewise function f(x) to find the following - $(f \circ f \circ f)(1)$

Solve the equation. - $\log _{5}(x+3)-\log _{5}(x-5)=4$

Solve. -Use the formula $\mathrm{N}=\mathrm{Ie}$ , $\mathrm{kt}$ , where $\mathrm{N}$ is the number of items at time $\mathrm{t}$ , $\mathrm{I}$ is the initial amount, and $\mathrm{k}$ is a growth constant equal to the percent of growth (expressed in decimal form) per unit of time. There are currently 56 million cars in a certain country, increasing by $4.1 \%$ annually. How many years will it take for this country to have 78 million cars? Round to the nearest year.

Graph f(x). State the domain, range, and horizontal asymptote of the function - $f(x)=3^{x-4}+1$

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _{\mathrm{x}} 24-\log _{\mathrm{X}} 8$

Solve. - $\log _{2}\left(\log _{4}(2 x+8)\right)=1$

Graph f(x). State the domain, range, and horizontal asymptote of the function - $f(x)=\left(\frac{1}{5}\right)^{x}+1$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=\frac{3}{x-9}$

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate. - $f(x)=-8 x+7 ; g(x)=-9 x^{2}+7 x-2$ Find $(\mathrm{g} \circ \mathrm{of})(6)$ .

Expand. A ssume that all variables represent positive real numbers. - $\log _{\mathrm{b}} \mathrm{yz}^{9}$

Evaluate. Round to the nearest thousandth, if necessary. - $\ln \left(\frac{1}{e^{6}}\right)$

Solve. - $\log x=3$

Evaluate. -

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers. - $\log _{5} \sqrt{6 x}$