log problems?

Question

log(x) + log(x-13)=log(15x)
plz solve for x

Answer 1

product rule:
log(a) + log(b) = log(ab)

log(x) + log(x - 13) = log(15x)

log(x^2 - 13x) = log(15x)

if log(a) = log(b), then a = b
x^2 - 13x = 15x

x^2 - 28x = x
x (x - 28) = x
x = 0 or 28

you can not take log of 0, so only 28 is the answer

Answer 2

First x-13 >0 so x>13
log x(x-13) = log 15x

so x^2-13x=15x) x^2-28x= 0 so x= 0 NO
and x= 28