# What is e^(ln(x)?

Oct 23, 2015

#### Answer:

It's $x$.

#### Explanation:

The logarithm and the exponential are inverse function, which means that if you combine them, you obtain the identity function, i.e. the function $I$ such that $I \left(x\right) = x$.

In terms of definitions, it becomes obvious. The logarithm $\ln \left(x\right)$ is a function which tells you what exponent you must give to $e$ to obtain $x$. So, ${e}^{\log \left(x\right)}$, literally means:

"$e$ to a power such that $e$ to that power gives $x$".