Logarithms and inequality problem?

(4^x - 2)log(1 - x^2) > 0

(4^x - 2) > 0 and log(1 - x^2) > 0; or (4^x - 2) < 0 and log(1 - x^2) < 0

4^x > 2 and 1 - x^2 > 1; or 4^x < 2 and 0 < 1 - x^2 < 1

2^(2x) > 2^1 and x^2 < 0; or 2^(2x) < 2^1 and -1 < -x^2 < 0

Note that x^2 >= 0, so we can ignore the first set of inequalities as they are not possible.

2x < 1 and 1 > x^2 > 0

x < 1/2 and -1 < x < 0 and 0 < x < 1

-1 < x < 0 and 0 < x < 1/2

(-1 , 0) U (0 , 1/2)