+130511 log2+log(11-x^2)-log(1-x)=0 subtract log(2) from both sides
log(11-x^2)-log(1-x) = - log 2 and we can use a property of logs to write
log [ (11 - x^2) / (1 -x)] = - log(2) which means that
10-log(2) = [11 - x^2] / [ 1 - x]
1/2 = [11 - x^2] / [ 1 - x ] multiply both sides by 1 - x
(1/2) [ 1 - x ] = 11 - x^2 multiply through by 2
1 - x = 22 - 2x^2 rearrange
2x^2 - x - 21 = 0 factor
(2x -7) (x + 3) = 0
Setting each factor to 0, the possible answers are x = 7/2 or x = -3
We must reject the first solution because it makes a log negative in the original equation
So...the only [real] solution is x = -3
