The value of log 0.0001 to the base 0.1 is:

1. 4

2. 3

3. $\dfrac{1}{4}$

4. $\dfrac{1}{3}$

Let,

⇒ log_0.1 (0.0001) = x

⇒ 0.0001 = 0.1^x

⇒ $\dfrac{1}{10000} = \Big(\dfrac{1}{10}\Big)^x$

⇒ $\dfrac{1}{10^4} = \Big(\dfrac{1}{10}\Big)^x$

⇒ $\Big(\dfrac{1}{10}\Big)^4 = \Big(\dfrac{1}{10}\Big)^x$

Equating the exponents,

⇒ x = 4.

Hence, option 1 is the correct option.