[tex]
log_{2}(\frac{x-1}{x+1}) + log_{2}({x}^{2}-1) = 4 \\
log_{2}(\frac{x-1}{x+1}.{x}^{2}-1) =log_{2}({2}^{4}) \\
log_{2}(\frac{(x-1)({x}^{2}-1)}{x+1}) =log_{2}(16) \\
\frac{(x-1)({x}^{2}-1)}{x+1}= 16 \\
\frac{(x-1)(x+1)(x-1)}{x+1} = 16 \\
{(x-1)}^{2} = 16 \\
x = - 3 \\x = 5 \\
[/tex]
