Solve for x: log4(x) + log4(16) = log4(512 − x) + 2

Answer 1

I assume the 4 is meant to be the base.

log₄x + log₄16 = log₄(512 - x) + 2

Note that

2 = log₄16 ⇒

log₄x + log₄16 = log₄(512 - x) + log₄16 ⇒

log₄x = log₄(512 - x)

Take 4⁽⁾ of both sides.

x = 512 - x

2x = 512

x = 256