# How do you solve for x?: log(x) - log(x-3)=-1

Oct 24, 2015

The equation represents an impossible situation; there is no solution for $x$

#### Explanation:

$\log \left(x\right)$ and $\log \left(x - 3\right)$ are only meaningful if $x > 0$ and $\left(x - 3\right) > 0$

Therefore
$\textcolor{w h i t e}{\text{XXX}} x > \left(x - 3\right)$
and
$\textcolor{w h i t e}{\text{XXX}} \log \left(x\right) > \log \left(x - 3\right)$

$\Rightarrow \log \left(x\right) - \log \left(x - 3\right) > 0$

Therefore $\log \left(x\right) - \log \left(x - 3\right)$ can not be $= - 1$