4. Inverse, Exponential, and Logarithmic Functions

Write the log expression as a single log.

${\log }_2\frac{1}{9x}+2{\log }_{2}3x$

Write the single logarithm as a sum or difference of logs.

${\log }_5\left(\frac{5{(2x+3)}^2}{x^3}\right)$

Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.

${\log }_{9}67$

Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log. 

${\log }_{2}3789$

Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.

${\log }_{3}17$

Write the single logarithm as a sum or difference of logs.

${\log }_3\left(\frac{\sqrt{x}}{9y^2}\right)$

Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.

${\log }_{8}41$

Write the log expression as a single log.

$\ln \frac{3x}{y}+2\ln 2y-\ln 4x$