4. Inverse, Exponential, and Logarithmic Functions

Solve the exponential equation.

${81}^{x+1}={27}^{x+5}$

Solve the exponential equation.

$2\cdot {10}^{3x}=5000$

Solve the exponential equation.

${100}^x={10}^{x+17}$

Solve the exponential equation.

$4^{x+7}=16$

Solve the exponential equation.

$e^{2x+5}=8$

Solve the exponential equation.

$7^{2x^2-8}=1$

Solve the logarithmic equation.

$\log (x+2)+\log 2=3$

Solve the logarithmic equation.

${\log }_7(6x+13)=2$

Solve the exponential equation.

$900={10}^{x+17}$

Solve the logarithmic equation.

${\log }_3(3x+9)={\log }_{3}5+{\log }_{3}12$