# How do you solve the equation 2log_3 sqrt(x) = log_3 (6x - 1)?

Mar 25, 2017

$\left\{\frac{1}{5}\right\}$

#### Explanation:

Use the following laws of logarithms to solve this problem:

$a \log n = \log {n}^{a}$
$\log n = \log m \to n = m$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We have:

${\log}_{3} {\left(\sqrt{x}\right)}^{2} = {\log}_{3} \left(6 x - 1\right)$

${\log}_{3} x = {\log}_{3} \left(6 x - 1\right)$

$x = 6 x - 1$

$1 = 5 x$

$x = \frac{1}{5}$

If you check in the equation, you will find this solution indeed works.

Hopefully this helps!