Question

How do you solve `log _4 (x)+ log _4 (x^2) =5`?

Answer 1

Use exponentiation with `4` to find:

`x = 4^(5/3) ~~ 10.0793684`

Explanation:

`x^3 = 4^(log_4(x^3)) = 4^(log_4(x * x^2)) = 4^(log_4(x) + log_4(x^2)) = 4^5`

So:

`x = root(3)(4^5) = (4^5)^(1/3) = 4^(5/3)`