Question 628409
log base 2 of (x) + log base 2 of (x+2)=log base 2 of (x+6) 

So we will have:

log base 2 of [x(x+2)] = log base 2 of (x + 6)
x(x +2) = x + 6
x^2 + 2x = x + 6
x^2 + x - 6= 0
(x +3)(x - 2) = 0
x = -3 or x = 2
We can NOT choose x = -3 because property of log x which x can not be negative.
Thus the ONLY solution is x = 2.
Hope it helps:)
John10