# How do you solve log_4 5 - log_4x = log_4(5/4)?

Oct 6, 2016

$x = 4$

#### Explanation:

${\log}_{4} 5 - {\log}_{4} x = {\log}_{4} \left(\frac{5}{4}\right)$

Condense two log terms into one log term
$\rightarrow$ If the logs are being subtracted, the values are being divided.

${\log}_{4} \left(\frac{5}{x}\right) = {\log}_{4} \left(\frac{5}{4}\right)$

Without any further working, we can see by inspection that

$x = 4$