# How do you find the exact value of lnroot4(e^3)?

Jan 4, 2017

$\frac{3}{4}$

#### Explanation:

Use $\sqrt[n]{{a}^{m}} = {a}^{\frac{m}{n}}$.

$= \ln \left({e}^{\frac{3}{4}}\right)$

Use the rule $\ln {a}^{n} = n \ln a$:

$= \frac{3}{4} \ln e$

Since $y = \ln x$ and $y = {e}^{x}$ are inverses, their product will be $1$.

$= \frac{3}{4}$

Hopefully this helps!