Solve and check for extraneous roots.

Question

log_2x+log_2(x+2)=3

* _2 is a subscript and (x+2) isn't a superscript*

Answer 1

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