Question

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

Answer 1

`{1/5}`

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!