2. If positive numbers $a, b$ satisfy $\log _{2} a+\log _{4} b=8, \log _{4} a+\log _{8} b=2$, then the value of $\log _{8} a+\log _{2} b$ is
According to the problem, $\left\{\begin{array}{l}\log _{2} a+\frac{1}{2} \log _{2} b=8, \\ \frac{1}{2} \log _{2} a+\frac{1}{3} \log _{2} b=2\end{array} \Rightarrow\left\{\begin{array}{l}\log _{2} a=20, \\ \log _{2} b=-24 .\end{array}\right.\right.$ Therefore, $\log _{8} a+\log _{2} b=\frac{1}{3} \log _{2} a+\log _{2} b=\frac{20}{3}-24=-\frac{52}{3}$.