Solve and check for extraneous roots.
log_2x+log_2(x+2)=3
* _2 is a subscript and (x+2) isn't a superscript*
So I read it as:
log2 x + log2(x+2) = 3
log2(x(x+2)) = 3
x(x+2) = 2^3
x^2 + 2x - 8 = 0
(x+4)(x-2) = 0
x = -4 OR x = 2
but in log x, x≥0 by definition
x = 2