log_{a} b − log_{a} c = log_{a} (b / c)
log_{a} x = b > a^{b} = x
~~~~~~~~~~~
log_{2} x^{2} − log_{2} (x + 5) = 2
log_{2} [x^{2} / (x + 5)] = 2
x^{2}
 = 2^{2}
x + 5
x^{2} = 4(x + 5)
x^{2}  4x  20 = 0
D = (4)^{2} +80 = 96
x_{12} = (4 ± √96) / 2
x_{1} = 2 + 2√6 > 0
x_{2} = 2 − 2√6 < 0 (logarithm is not exist for negative numbers and 0)
x = 2(1 + √6) is the answer.
10/22/2013

Nataliya D.