i need logrithms help!!?

Question

please help me solve:

logX + log (X+15) = 2
thankyou...

Answer 1

First, let's combine the logs:
log (x * (x+15)) = 2

Then use both sides of the equation as exponents of 10, to get rid of the logarithm:
10^(log(x*(x+15)) = 10^2
x*(x+15) = 100
x^2 + 15x = 100
x^2 + 15x -100 = 0

This factors nicely into:
(x+20)*(x-5) = 0

Hence, the two possible answers are x=-20 and x=5.

Hope that helps!