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}$

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

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

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume x > 0 and y > 0.

b. ln 0 = 1

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume x > 0 and y > 0.

c. ln (x + y) = ln x + ln y

Logarithm properties Use the integral definition of the natural logarithm to prove that ln(x/y) = ln x - ln y.