# Are lne and lne^x the same?

Feb 16, 2017

No

#### Explanation:

As $\ln$ is the natural logarithm then is is a logarithm using base $e$ and therefore we can directly evaluate the two expressions as:

$\ln e \setminus \setminus = 1$
$\ln {e}^{x} = x$

These are clearly not the same.

If we could not directly evaluate then we can use the fact that for any base $b$ then:

${\log}_{b} A = {\log}_{b} B \iff A = B$

and again it is clear that $e$ and ${e}^{x}$ are not identical.