# How do you solve e^lnx=12?

May 8, 2016

$x = 12$

#### Explanation:

$\textcolor{red}{\ln \left(x\right)}$ means $\textcolor{red}{\text{ the value "k" you need as an exponent of e for " e^k" to be equal to x}}$

Therefore
$\textcolor{w h i t e}{\text{XXX}} {\textcolor{b l u e}{e}}^{\textcolor{red}{\ln \left(x\right)}}$
means
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{e}$ raised to the exponent of $\textcolor{red}{\text{ the value "k" you need as an exponent of e for " e^k" to be equal to x}}$

While this is a bit of a mind twister, if you think it though, what this means is that
$\textcolor{w h i t e}{\text{XXX}} {e}^{\ln \left(x\right)} = x$