# What is the natural log of infinity?

##### 1 Answer
Sep 21, 2014

The answer is $\infty$.

The natural log function is strictly increasing, therefore it is always growing albeit slowly. The derivative is $y ' = \frac{1}{x}$ so it is never 0 and always positive.

You can also look at it as:

$n = \ln \infty$
${e}^{n} = \infty$
Therefore, $n$ must be large.