Question

Find the value of \(\log_{0.1} 0.01\)

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The Correct Option is B

To solve the problem, we need to evaluate the logarithmic expression \( \log_{0.1} 0.01 \).

1. Understanding the Logarithmic Identity:
Recall that \( \log_b a = x \) means \( b^x = a \). So we want to find the power to which 0.1 must be raised to get 0.01.

2. Converting to Powers of 10:
We know:

• \( 0.1 = 10^{-1} \)
• \( 0.01 = 10^{-2} \)

So, the expression becomes:
\( \log_{10^{-1}} 10^{-2} \)

3. Using Change of Base Formula:
We apply the formula:
\( \log_b a = \frac{\log a}{\log b} \)

So: \[ \log_{10^{-1}} 10^{-2} = \frac{\log 10^{-2}}{\log 10^{-1}} = \frac{-2}{-1} = 2 \]

Final Answer:
The value of \( \log_{0.1} 0.01 \) is 2 (Option B).