How do I find the inverse of $e^{x}$ $e^x$ ?

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Answer 1 · 2014-09-05T02:43:44

The answer is $y = ln x$ $y=ln x$ .

We find the answer the same way we find any inverse; we swap $x$ $x$ and $y$ $y$ then solve.

$y = e^{x}$ $y=e^x$
$x = e^{y}$ $x=e^y$ swap
$ln x = ln (e^{y})$ $ln x=ln (e^y)$ take logarithm of both sides
$ln x = y$ $ln x=y$

$ln$ $ln$ and $e$ $e$ functions cancel each other because they are inverses.

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