# How do you solve log_2 (x+2) - log_2(x) =8?

Sep 18, 2015

I found: $x = \frac{2}{255} = 0.007843$

#### Explanation:

You can use first a rule of the log that says:
$\log x - \log y = \log \left(\frac{x}{y}\right)$
and get:
${\log}_{2} \left[\frac{x + 2}{x}\right] = 8$
Then you use the definition of log to get:
$\frac{x + 2}{x} = {2}^{8}$
rearranging:
$x + 2 = 256 x$
$255 x = 2$
$x = \frac{2}{255} = 0.007843$