The value of log₅ 125 ÷ log₅ $\sqrt{5}$ is :

1. 5

2. 120

3. 6

4. 60

Given,

$\Rightarrow \text{log}${5} \space 125 ÷ \text{log}{5} \space \sqrt{5} \\[1em] \Rightarrow \text{log}{5} \space 5^3 ÷ \text{log}{5} \space (5)^{\dfrac{1}{2}} \\[1em] \Rightarrow 3 \times \text{log}{5} \space 5 ÷ \dfrac{1}{2} \times \text{log}{5} \space 5 \\[1em] \Rightarrow 3 \times 1 ÷ \dfrac{1}{2} \times 1 \\[1em] \Rightarrow 3 ÷ \dfrac{1}{2} \\[1em] \Rightarrow 3 \times 2 \\[1em] \Rightarrow 6.

Hence, Option 3 is the correct option.