# How do you solve  2 log 3 + log x = log 36?

Feb 7, 2016

See solution below.

#### Explanation:

We can start the solving process by using the log rule $b \log n = \log {n}^{b}$

$\log 9 + \log x - \log 36 = 0$

Using the property ${\log}_{a} n + {\log}_{a} m = {\log}_{a} \left(n \times m\right)$ and ${\log}_{a} n - {\log}_{a} m = {\log}_{a} \left(\frac{n}{m}\right)$ we can continue the solving process.

$\log \left(\frac{9 \times x}{36}\right)$ = 0

Convert to exponential form

$\frac{9 x}{36} = {10}^{0}$

9x = $1 \times 36$

x = 4

Hopefully this helps!