Help solving a log problem?

Question

Can somebody help me solve this? I can't just use my calculator. Could you be so kind as to show me the steps.

log X + log (X + 15) = 2

Answer 1

Take logs to base ten:-
log [ x (x + 15) ] = 2
x (x + 15) = 10²
x² + 15x - 100 = 0
(x + 20) (x - 5) = 0
x = 5 (accepting + ve value for x)

Answer 2

I won't give you the anwser but see if this helps. Conbine terms, take the antilog and I think you can solve the problem.
PhD Food Chemistry and Nutrition