Posted by Joy on .
If f(x) = log2 (x  2)3 and g(x) = log8 (x  2), when is (f + g)(x) = 0?

Discrete Mathematics 
Steve,
working with logs base 2,
since 8=2^3, g(x) = 1/3 log(x2)
(f+g)(x) = f(x)+g(x)
= 3log(x2) + 1/3 log(x2)
= 10/3 log(x2)
so, if (f+g)(x) = 0,
log(x2) = 0
x2 = 1
x = 3
check
log_2(32)^3 = 0
log_8(32) = 0 
Discrete Mathematics 
Joy,
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.