0. Functions

Solve the exponential equation.

$4^{x+7}=16$

Solve the exponential equation.

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

Solve the exponential equation.

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

Solve the exponential equation.

$2\cdot10^{3x}=5000$

Solve the exponential equation.

$900=10^{x+17}$

Solve the exponential equation.

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

Solve the exponential equation.

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

Solve the logarithmic equation.

$\log_3\left(3x+9\right)=\log_35+\log_312$

Solve the logarithmic equation.

$\log\left(x+2\right)+\log2=3$

Solve the logarithmic equation.

$\log_7\left(6x+13\right)=2$

Use the graph of ƒ to find ƒ⁻¹ (2),ƒ⁻¹ (9), and ƒ⁻¹ (12) <IMAGE>

Find the inverse of the function ƒ(x) = 2x. Verify that ƒ(ƒ⁻¹(x)) = x and ƒ⁻¹(ƒ(x)) = x .

Sketch the graph of the inverse of ƒ. <IMAGE>

Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.

ƒ(x) = |2x + 1|

Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.

{Use of Tech} ƒ(x) = 1/(x-5)