지수함수와 로그함수 전체 문제

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

Find the inverse of the function $f(x)={x}^{5}-9.$

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

Solve the equation ${2}^{2x-4}=64.$

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

Megan invested $\char36 21,000$ in a savings account. If the interest rate is $5\%,$ 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: ${10}^{-2}=\frac{1}{100}.$

Convert the equation from logarithmic equation to exponential form: $3={\log }_{7}343$

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

Evaluate ${\log }_{11}1.$

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

Graph the function $y={\log }_{3}x.$

Solve for x: $\log ({x}^{2}-39)=1$

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

Evaluate each. ⓐ ${6}^{{\log }_{6}17}$ ⓑ ${\log }_{9}{9}^{-3}$

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

${\log }_{5}25ab$

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

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

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

${\log }_{2}\sqrt[4]{\frac{5{x}^{3}}{16{y}^{2}{z}^{7}}}$

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

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

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

$\frac{1}{6}\log \,x-3\log (x+5)$