log 2 (x+5) + log 2 (x+2) = log 2 (x+6)

 log 2 (x+5) + log 2 (x+2) = log 2
(x+6)

We know that log x + log y = log
x*y

==> log 2 (x+5)(x+2) = log 2
(x+6)

We know that if log x = log y ==>
x=y

==> (x+5)(x+2) =
(x+6)

Open
brackets:

==> x^2 + 7x + 10 =
x+6

==> X^2 + 6X + 4
=0

==> x =[ -6 +
sqrt(36-16)]/2

           = [-6 + sqrt(20)] /
2

           = [-6 +
2sqrt(5)]/2

            = -3 +
sqrt(5)

==> the answer is x = -3 +
sqrt(5)