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

Mar 29, 2016

$\log \left(x + 14\right)$

#### Explanation:

$\log \left({x}^{2} - 196\right) = \log \left({x}^{2} - {14}^{2}\right) = \log \left(\left(x - 14\right) \cdot \left(x + 14\right)\right)$
$\log x + \log \left(\left(x - 14\right) \left(x + 14\right)\right) - \log 2 - \log \left(x - 14\right)$

$\log x + \cancel{\log \left(x - 14\right)} + \log \left(x + 14\right) - \log 2 - \cancel{\log \left(x - 14\right)}$

$\log x + \log \left(x + 14\right) - \log x$

$\log \left(x \cdot \left(x + 14\right)\right) - \log x$

$\log \left({x}^{2} + 14 x\right) - \log x$

$\log \left(\frac{{x}^{2} + 14 x}{x}\right)$

$\log \left(x + 14\right)$