7.054. $\log _{2} x+\log _{4} x+\log _{8} x=11$.
## Solution.

Domain: $x>0$.

We have $\log _{2} x+\frac{1}{2} \log _{2} x+\frac{1}{3} \log _{2} x=11, \log _{2} x=6$, from which $x=2^{6}=64$.

Answer: 64.