Evaluate :

log₃ 8 ÷ log₉ 16

Simplifying the expression,

$\Rightarrow \text{log}$3 \space 8 ÷ \text{log}9 \space 16 \\[1em] \Rightarrow \dfrac{\text{log 8}}{\text{log 3}} ÷ \dfrac{\text{log 16}}{\text{log 9}} \\[1em] \Rightarrow \dfrac{\text{log 8}}{\text{log 3}} \times \dfrac{\text{log 9}}{\text{log 16}} \\[1em] \Rightarrow \dfrac{\text{log 2}^3}{\text{log 3}} \times \dfrac{\text{log 3}^2}{\text{log 2}^4} \\[1em] \Rightarrow \dfrac{\text{3 log 2}}{\text{log 3}} \times \dfrac{\text{2 log 3}}{\text{4 log 2}} \\[1em] \Rightarrow \dfrac{\text{6 log 2.log 3}}{\text{4 log 2.log 3}} \\[1em] \Rightarrow \dfrac{6}{4} \\[1em] \Rightarrow \dfrac{3}{2} \\[1em] \Rightarrow 1\dfrac{1}{2}.

Hence, log₃ 8 ÷ log₉ 16 = $1\dfrac{1}{2}$.