0. Functions

Which operation can be used to eliminate a natural logarithm, such as $\ln \left(x\right)$, from an equation?

Convert the following logarithmic expression to its equivalent exponential form.

$\log_4x=5$

Convert the following logarithmic expression to its equivalent exponential form.

$x=\log9$

Convert the following exponential expression to its equivalent logarithmic form.

$3^{x}=7$

Convert the following exponential expression to its equivalent logarithmic form.

$e^9=x+3$

{Use of Tech} Let f(x) = ln((x+1)/(x-1)) and g(x) = ln ((x+1)/(x-1)).

b. Sketch graphs of f and g to show that these functions do not differ by a constant.

Convert the following expressions to the indicated base.

$2^x$ using base e

Solving equations Solve the following equations.

log₈ x = 1/3

Find the inverse $f^{-1}\left(x\right)$ of each function (on the given interval, if specified).

$f\left(x\right)=e^{2x+6}$

What are the domain and range of ln x?

What is the inverse function of ln x, and what are its domain and range?