what 's the anwers with demonstration if possible.

Question

log₄ (X+2)+log₄(x-4)=2?

Answer 1

log₄(x+2) + log₄(x-4) = 2

log₄[(x+2)(x-4)] = 2

(x+2)(x-4) = 4²

So, x² - 2x - 24 = 0

(x - 6)(x + 4) = 0

x = 6 or x = -4

-4 is extraneous, so x = 6.