Question 867254
 Solve
a){{{log(2,(x+1)) + log(2,(x-1)) = 3}}}
addition of logs, is multiply
{{{log(2,((x+1)(x-1))) = 3}}}
FOIL
{{{log(2,(x^2-1)) = 3}}}
Write exponent equiv of logs
x^2 -1 = {{{2^3)}}}
x^2 - 1 = 8
x^2 - 1 - 8 = 0
x^2 - 9 = 0
Factors to
(x-3)(x+3) = 0
x = +3, is the only solution (no negative allowed in a log)
:
b){{{log(2,(x+2)) = 2 - log(2,(x-1))}}} 
{{{log(2,(x+2)) + log(2,(x-1))= 2}}}
{{{log(2,((x+2)(x-1))) = 2}}}
{{{log(2,(x^2+x-2)) = 2}}}
The exponent equiv
x^2 + x - 2 = {{{2^2}}}
x^2 + x - 2 = 4
x^2 + x - 2 - 4 = 0
x^2 + x - 6 = 0
Factors to
(x+3)(x-2) = 0
x = 2, the positive solution all we want here