Algebraically determine the value(s) of x: log9(x-5)=1-log9(x+3)

Question

Please help me. Thanks!

Answer 1

log9(x-5)=1-log9(x+3)
log9[(x-5)(x+3) =

(x-5)(x+3) = 9^1
x^2 - 2x - 24 = 0
(x-6)(x+4) = 0
x = 6 or -4

but x=-4 would be give an undefined result in the original, so
x = 6