Posted by **Joy** on Tuesday, July 30, 2013 at 4:50am.

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

- Discrete Mathematics -
**Steve**, Tuesday, July 30, 2013 at 4:53am
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

- Discrete Mathematics -
**Joy**, Tuesday, July 30, 2013 at 6:36am
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.

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