Solve: log x + log(x+15)=2

Answer 1

using the rule:
log (AB) = logA + logB

log x + log(x+15)=2
log(x(x+15)) = 2
x(x+15) = 10^2
x^2 + 15x - 100 = 0
(x + 20)(x-5) = 0
x = -20 or x = 5
BUT if x = -20 , we would have log (-20) in our expression, and log(a negative) is undefined

so , x = 5