State, true or false :

If $\dfrac{\text{log 25}}{\text{log 5}}$ = log x, then x = 2

Given,

$\dfrac{\text{log 25}}{\text{log 5}}$ = log x

Solving the equation, we get :

$\Rightarrow \dfrac{\text{log 25}}{\text{log 5}} = \text{log x} \\[1em] \Rightarrow \dfrac{\text{log 5}^2}{\text{log 5}} = \text{log x} \\[1em] \Rightarrow \dfrac{\text{2 log 5}}{\text{log 5}} = \text{log x} \\[1em] \Rightarrow \text{log x} = 2 \\[1em] \Rightarrow x = 10^2 = 100.$

Since, x is not equal to 2.

Hence, the statement $\dfrac{\text{log 25}}{\text{log 5}}$ = log x, then x = 2 is false.