Answer
$3$
Work Step by Step
RECALL:
The change-of-base formula for logarithms:
$\log_a{b} = \dfrac{\log{b}}{\log{a}}$
Use the change-of-base formula above to find:
$=\dfrac{\log{4}}{\log{2}} \cdot \dfrac{\log{6}}{\log{4}} \cdot \dfrac{\log{8}}{\log{6}}$
Cancel the common factors:
$\require{cancel}
=\dfrac{\cancel{\log{4}}}{\log{2}} \cdot \dfrac{\cancel{\log{6}}}{\cancel{\log{4}}} \cdot \dfrac{\log{8}}{\cancel{\log{6}}}
\\=\dfrac{\log{8}}{\log{2}}
\\=\dfrac{\log{2^3}}{\log{2}}$
Use the rule $\log{(M^r)}=r \cdot \log{M}$ to obtain:
$=\dfrac{3\cdot\log{2}}{\log{2}}$
Cancel common factors to obtain:
$\require{cancel}
=\dfrac{3\cancel{\log{2}}}{\cancel{\log{2}}}
\\=3$
