### Practice Test

For the functions, $f\left(x\right)=6x+1$ and $g\left(x\right)=8x-3,$ find ⓐ $\left(f\circ g\right)\left(x\right),$ ⓑ $\left(g\circ f\right)\left(x\right),$ and ⓒ $\left(f\xb7g\right)\left(x\right).$

Determine if the following set of ordered pairs represents a function and if so, is the function one-to-one. $\left\{\left(\mathrm{-2},2\right),\left(\mathrm{-1},\mathrm{-3}\right),\left(0,1\right),\left(1,\mathrm{-2}\right),\left(2,\mathrm{-3}\right)\right\}$

Graph, on the same coordinate system, the inverse of the one-to-one function shown.

Graph the function $g\left(x\right)={2}^{x-3}.$

Solve the equation $\frac{{e}^{{x}^{2}}}{{e}^{4}}={e}^{3x}.$

Megan invested $\text{\$}\mathrm{21,000}$ in a savings account. If the interest rate is $5\text{\%},$ how much will be in the account in 8 years by each method of compounding?

ⓐ compound quarterly

ⓑ compound monthly

ⓒ compound continuously.

Convert the equation from exponential to logarithmic form: ${10}^{\mathrm{-2}}=\frac{1}{100}.$

Solve for *x*: ${\text{log}}_{5}x=\mathrm{-3}$

Evaluate ${\text{log}}_{4}\frac{1}{64}.$

Solve for *x*:

$\text{log}({x}^{2}-39)=1$

What is the decibel level of a small fan with intensity ${10}^{\mathrm{-8}}$ watts per square inch?

Evaluate each. ⓐ
${6}^{{\text{log}}_{6}17}$

ⓑ
${\text{log}}_{9}{9}^{\mathrm{-3}}$

In the following exercises, use properties of logarithms to write each expression as a sum of logarithms, simplifying if possible.

$\text{ln}\frac{{e}^{12}}{8}$

In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.

$5{\text{log}}_{4}x+3{\text{log}}_{4}y$

Rounding to three decimal places, approximate ${\text{log}}_{4}73.$

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places.

${\left(\frac{1}{5}\right)}^{x}=9$

Jacob invests $14,000 in an account that compounds interest quarterly and earns $4\text{\%}.$ How long will it take for his money to double?

Researchers recorded that a certain bacteria population grew from 500 to 700 in 5 hours. At this rate of growth, how many bacteria will there be in 20 hours?

A certain beetle population can double in 3 months $\left(A=2{A}_{0}\right).$ How long will it take for that beetle population to triple?