# How do you solve log_6 x+log_6 9=log_6 54?

Oct 29, 2016

Answer is $x = 6$

#### Explanation:

${\log}_{6} x + {\log}_{6} 9 = {\log}_{6} 54$
$\therefore$$\log x + \log 9 = \log 54$
$\therefore \log x + \log {3}^{2} = \log 27 + \log 2$
$\therefore \log x + 2 \log 3 = 3 \log 3 + \log 2$
$\therefore \log x = \log 2 + \log 3$
$\therefore \log x = \log 6$
$\therefore x = 6$. (answer).