Question

How do you solve `log_8 25= 2log_8 x`?

Answer 1

`x = 5`

Explanation:

Rearrange using laws of logarithms, where a coefficient outside a `log` is the same as a power inside it.

`log_8 25 = 2log_8 x = log_8 x^2`

Raise both sides by eight,

`8^(log_8 25) = 8^(log_8 x^2)`
`25 = x^2`

which gives `x = -5, 5`.

But you can't have a `log` of a negative number, which just leaves `5`.