# How do you solve ln4-lnx=10?

Nov 29, 2015

$x = \frac{4}{{e}^{10}} = \approx 1.82 \times {10}^{- 4}$

#### Explanation:

$\ln \left(4\right) - \ln \left(x\right) = 10$

$\textcolor{w h i t e}{\text{XXXXXXXXXX}}$since $\log \left(\frac{a}{b}\right) = \log \left(a\right) - \log \left(b\right)$
$\Rightarrow \ln \left(\frac{4}{x}\right) = 10$

$\textcolor{w h i t e}{\text{XXXXXXXXXX}}$taking each side of the above as an exponent of $e$
$\Rightarrow \frac{4}{x} = {e}^{10}$

$\textcolor{w h i t e}{\text{XXXXXXXXXX}}$algebraic simplification
$\Rightarrow x = \frac{4}{{e}^{10}}$