How do you solve the problem below for x using substitution?

Question

log₄x=(log₄x²)²

Answer 1

log₄x = (log₄x²)²

Now log₄x² = 2log₄x

log₄x = (2 log₄x)²

log₄x = 4(log₄x)²

Now substitute u = log₄x:

u = 4u²

0 = 4u² - u

0 = u(4u-1)

u = 0 and u = 1/4

Substitute back log₄x = u:

log₄x = 0 This is undefined since 0 is outside of the domain of log₄x. Let's try the other solution:

log₄x = 1/4

x = 4^1/4 = (4^1/2)^1/2 = 2^1/2 = √2