$7.33 \log _{2} x+\log _{4} x+\log _{8} x=11$.
7.33 Using formula (7.7), we get the equation

$$
\log _{2} x+\frac{\log _{2} x}{\log _{2} 4}+\frac{\log _{2} x}{\log _{2} 8}=11, \text { or } \log _{2} x\left(1+\frac{1}{2}+\frac{1}{3}\right)=11
$$

from which $\log _{2} x=6$, i.e., $x=64$.

Answer: $x=64$.