State, true or false :

$\dfrac{\text{log x}}{\text{log y}}$ = log x - log y

Given,

$\dfrac{\text{log x}}{\text{log y}}$ = log x - log y

Solving R.H.S. of the above equation, we get :

⇒ log x - log y

⇒ log $\dfrac{x}{y}$.

Since, L.H.S. ≠ R.H.S.

Hence, the statement $\dfrac{\text{log x}}{\text{log y}} = \text{log x} - \text{log y}$ is false.