3A. Solve the equation

$$
2^{3 x}-\frac{8}{2^{3 x}}-6\left(2^{x}-\frac{1}{2^{x-1}}\right)=1
$$
Solution. We introduce the substitution $t=2^{x}$. By substituting into the given equation, we obtain the equation $t^{3}-\frac{8}{t^{3}}-6\left(t-\frac{2}{t}\right)=1$, which is equivalent to the equation $\left(t-\frac{2}{t}\right)^{3}=1$. From the last equation, we get $t-\frac{2}{t}=1$, from which $t=-1$ or $t=2$. Given the substitution, $t$ is a positive number, so $t=2$, from which we obtain $x=1$.

It is easily verified that $x=1$ is indeed a solution to the given equation.