Given log_x 25 - log_x 5 = 2 - log_x $\dfrac{1}{125}$; find x.

Given,

⇒ log_x 25 - log_x 5 = 2 - log_x $\dfrac{1}{125}$

⇒ log_x 25 - log_x 5 + log_x $\dfrac{1}{125}$ = 2

⇒ log_x $\dfrac{25 \times \dfrac{1}{125}}{5}$ = 2

⇒ log_x $\dfrac{25}{625}$ = 2

⇒ x² = $\dfrac{25}{625}$

⇒ $x^2 = \dfrac{1}{25}$

⇒ x = $\sqrt{\dfrac{1}{25}} = \dfrac{1}{5}$.

Hence, x = $\dfrac{1}{5}$.