How do I solve log x + log (x-15)=2 ?

Note that one property of logarithms is that

log(a) + log(b) = log(ab)

for all logarithmic bases.

Now assuming that by log you are referring to base 10, since without the subscript, it is implied.

But

log(x) + log(x - 15) = 2

log(x(x - 15)) = 2

x(x - 15) = 10²

x² - 15x - 100 = 0

x = (15 ± √((-15)² - 4*1*(-100)))/(2*1)

= (15 ± √(225 + 400))/2

= (15 ± √(625))/2

= (15 ± 25)/2

Since log(a) is undefined for a ≤ 0.we must have that

x = (15 + 25)/2

ie

x = 20

I got lost looking at that. Is that the quadratic formula?