If f(x) = log2 (x - 2)3 and g(x) = log8 (x - 2), when is (f + g)(x) = 0?

Answer 1

working with logs base 2,
since 8=2^3, g(x) = 1/3 log(x-2)

(f+g)(x) = f(x)+g(x)
= 3log(x-2) + 1/3 log(x-2)
= 10/3 log(x-2)

so, if (f+g)(x) = 0,
log(x-2) = 0
x-2 = 1
x = 3

check

log_2(3-2)^3 = 0
log_8(3-2) = 0

Answer 2

Thanks Steve! I am starting to write these down so that way I will understand them. It is easier for me to go off an example. I appreciate all your help.