(14) Solve the inequality
$$
\log _{2}\left(x^{12}+3 x^{10}+5 x^{8}+3 x^{6}+1\right)<1+\log _{2}\left(x^{4}+1\right) .
$$
(14) Method 1: From
$$
1+\log _{2}\left(x^{4}+1\right)=\log _{2}\left(2 x^{4}+2\right),
$$

and $\log _{2} y$ is an increasing function on $(0,+\infty)$, hence the original inequality is equivalent to
$$
x^{12}+3 x^{10}+5 x^{8}+3 x^{6}+1x^{6}+3 x^{4}+3 x^{2}+1+2 x^{2}+2 \\
& =\left(x^{2}+1\right)^{3}+2\left(x^{2}+1\right)
$$

Then
$$
\left(\frac{1}{x^{2}}\right)^{3}+2\left(\frac{1}{x^{2}}\right)>\left(x^{2}+1\right)^{3}+2\left(x^{2}+1\right) \text {. }
$$

Let $g(t)=t^{3}+2 t$, then the inequality is transformed into $g\left(\frac{1}{x^{2}}\right)>g\left(x^{2}+1\right)$, clearly $g(t)=$ $t^{3}+2 t$ is an increasing function on $\mathbf{R}$, thus the original inequality is equivalent to $\frac{1}{x^{2}}>x^{2}+1$, i.e., $\left(x^{2}\right)^{2}+$ $x^{2}-1<0$, solving this yields $x^{2}<\frac{\sqrt{5}-1}{2}$, hence the solution set of the original inequality is $\left(-\sqrt{\frac{\sqrt{5}-1}{2}}, \sqrt{\frac{\sqrt{5}-1}{2}}\right)$