3B. Solve the equation $\log _{x} 2-\log _{4} x+\frac{7}{6}=0$.
Solution. The domain $D$ of the equation is defined by $x>0, x \neq 1$. The given equation is equivalent to

$$
\log _{x} 2-\frac{1}{\log _{x} 2^{2}}+\frac{7}{6}=0
$$

or equivalently,

$$
\log _{x} 2-\frac{1}{2 \log _{x} 2}+\frac{7}{6}=0
$$

We introduce the substitution $\log _{x} 2=t$, which transforms the last equation into $6 t^{2}+7 t-3=0$, with solutions $t_{1}=\frac{1}{3}$ and $t_{2}=-\frac{3}{2}$.

Finally, returning to the substitution, we get $x=8$ and $x=\frac{\sqrt[3]{2}}{2}$, values that belong to the domain of the original equation, and are therefore its solutions.