Answer
$2$
Work Step by Step
RECALL:
(1)The change-of-base formula for logarithms:
$\log_a{b} = \dfrac{\log{b}}{\log{a}}$
(2) $\log_a{(B^n)}=n\cdot\log_a{B}$
Use rule (1) above to obtain:
$\log_3{8} \cdot \log_8{9}=\dfrac{\log{8}}{\log{3}} \cdot
\dfrac{\log{9}}{\log{8}}$
Cancel the common factors to obtain:
$\require{cancel}
=\dfrac{\cancel{\log{8}}}{\log{3}} \cdot
\dfrac{\log{9}}{\cancel{\log{8}}}
\\=\dfrac{\log{9}}{\log{3}}
\\=\dfrac{\log{3^2}}{\log{3}}$
Use rule (2) above to obtain:
$=\dfrac{2\log{3}}{\log{3}}$
Cancel the common factors to obtain:
$\require{cancel}
=\dfrac{2\cancel{\log{3}}}{\cancel{\log{3}}}
\\=2$
