# How do you solve ln e^(sqrt{2})?

Oct 18, 2016

The value of this expression is $\sqrt{2}$

#### Explanation:

This question ca be answered using the definition of logarythm (here natural $\ln$))

According to a definition:

## ${\log}_{a} b = c \iff {a}^{c} = b$

So we are looking for a number to which the base has to be risen to get the value of $b$.

In the given example we are looking for a number to which we have to raise $e$ to get the number ${e}^{\sqrt{2}}$. From the form of the number ${e}^{\sqrt{2}}$ we can see that the answer is $\sqrt{2}$.