# How do you evaluate ln sqrt(e)?

Apr 10, 2016

$\frac{1}{2}$

#### Explanation:

Recall that: sqrtn=n^(1/2:

We can now express your equation as:
$\ln \sqrt{e} = \ln {e}^{\frac{1}{2}}$

Recall that: ${\log}_{n} {a}^{m} = m {\log}_{n} a$

We can further simplify the given equation:

$\ln {e}^{\frac{1}{2}} = \frac{1}{2} \ln e$

Recall that: $\ln e = {\log}_{e} e = 1$

We can now say that:

$\frac{1}{2} \ln e = \frac{1}{2} \left(1\right) = \frac{1}{2}$

Therefore, $\ln \sqrt{e} = \frac{1}{2}$