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

##### 1 Answer

Mar 25, 2017

#### Explanation:

*Use the following laws of logarithms to solve this problem*:

#alogn = logn^a#

#logn = logm -> n = m#

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

We have:

#log_3 (sqrt(x))^2 =log_3(6x - 1)#

#log_3 x = log_3(6x - 1)#

#x = 6x - 1#

#1 = 5x#

#x = 1/5#

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

Hopefully this helps!