Answer
$2$
Work Step by Step
We know that $\log_a {b}=\dfrac{\log_c {b}}{\log_c {a}}$.
Hence,
$\log_3 {8}\cdot \log_8 {9}
\\=\dfrac{\log{8}}{\log{3}}\cdot\dfrac{\log{9}}{\log{8}}
\\=\dfrac{\log{9}}{\log{3}}
\\=\log_3 {9}
\\=\log_3 {(3^2)}$
Use the rule $\log_a{a^x}=x$ to obtain:
$\log_3{(3^2)}=2$
