If $\dfrac{\text{log }125}{\text{log } \dfrac{1}{5}}$ = log x, the value of x is :

1. 0.001

2. 0.01

3. 25

4. 5

Given,

$\Rightarrow \dfrac{\text{log }125}{\text{log } \dfrac{1}{5}} = \text{log x} \\[1em] \Rightarrow \dfrac{\text{log }5^3}{\text{log } 5^{-1}} = \text{log x} \\[1em] \Rightarrow \dfrac{3\text{log }5}{-1\text{log } 5} = \text{log x} \\[1em] \Rightarrow -3 = \text{log x} \\[1em] \Rightarrow x = 10^{-3} \\[1em] \Rightarrow x = \dfrac{1}{10^3} \\[1em] \Rightarrow x = \dfrac{1}{1000} \\[1em] \Rightarrow x = 0.001$

Hence, Option 1 is the correct option.