Expand the Logarithmic Expression log base 3 of 5* log base 2 of 3* log base 5 of 16

$\log_{3} (5) \cdot \log_{2} (3) \cdot \log_{5} (16)$

Rewrite $\log_{5} (16)$ as $\log_{5} (2^{4})$ .

$\log_{3} (5) \log_{2} (3) \cdot \log_{5} (2^{4})$

Expand $\log_{5} (2^{4})$ by moving $4$ outside the logarithm.

$\log_{3} (5) \log_{2} (3) \cdot (4 \log_{5} (2))$

Move $4$ to the left of $\log_{3} (5) \log_{2} (3)$ .

$4 \log_{3} (5) \log_{2} (3) \log_{5} (2)$