# How do you simplify log x + log (x^2 - 196) - log 2 - log (x - 14)?

Jun 1, 2018

$\log \left(\frac{x \cdot \left({x}^{2} - 16\right)}{2 \cdot \left(x - 14\right)}\right)$

#### Explanation:

We write
$\log \left(x\right) + \log \left({x}^{2} - 16\right) - \left(\log \left(2\right) + \log \left(x - 14\right)\right)$
and this is
$\log \left(x \cdot \left({x}^{2} - 16\right)\right) - \log \left(2 \left(x - 14\right)\right)$
This is
$\log \left(\frac{x \left({x}^{2} - 16\right)}{2 \cdot \left(x - 14\right)}\right)$
We have used that
$\log \left(a b\right) = \log \left(a\right) + \log \left(b\right)$
$\log \left(\frac{a}{b}\right) = \log \left(a\right) - \log \left(b\right)$
for $a , b > 0$