# How do you solve for x?: log_3 (x-2) + log_3 (x-4) = 2

Oct 26, 2015

I found $x = 6.1623$

#### Explanation:

We can combine the two logs as:
${\log}_{3} \left[\left(x - 2\right) \left(x - 4\right)\right] = 2$
Use the definition of log to get:
$\left(x - 2\right) \left(x - 4\right) = {3}^{2}$
${x}^{2} - 4 x - 2 x + 8 = 9$
${x}^{2} - 6 x - 1 = 0$
${x}_{1 , 2} = \frac{6 \pm \sqrt{36 + 4}}{2} =$ two solutions:
${x}_{1} = 6.1623$
${x}_{2} = - 0.1623$ NO