Find the value of : log_0.2 5

Let log_0.2 5 = x.

∴ (0.2)^x = 5

⇒ $\Big(\dfrac{2}{10}\Big)^x = 5$

⇒ $\Big(\dfrac{1}{5}\Big)^x = 5$

⇒ 5^-x = 5

⇒ x = -1

Hence, log_0.2 5 = -1.