Question

How do you solve `\log _ { 8} ( 3x ^ { 2} ) = 2\log _ { 8} ( 3x )`?

Answer 1

This equation has no solutions

Explanation:

Given:

`log_8(3x^2) = 2log_8(3x)`

Apply the exponential function `f(t) = 8^t` both sides to get:

`3x^2 = 8^(log_8(3x^2)) = 8^(2log_8(3x)) = (3x)^2 = 9x^2`

The derived equation `3x^2=9x^2` only has one solution, namely `x=0`, but `log_b 0` is undefined for any base `b`.

So the original equation has no solutions.