Question

If \(\log_m m + \log_{\frac{1}{6}} \frac{1}{3} = 2\), then \(m\) is equal to

• A. 4
• B. 24
• C. 12
• D. 18

Hint:

Use the change of base formula and properties of logarithms to simplify logarithmic equations.

Answer 1

The Correct Option is C

We are given the equation \(\log_m m + \log_{\frac{1}{6}} \frac{1}{3} = 2\). We know that \(\log_m m = 1\). Now we simplify \(\log_{\frac{1}{6}} \frac{1}{3}\) using the change of base formula: \[ \log_{\frac{1}{6}} \frac{1}{3} = \frac{\log \frac{1}{3}}{\log \frac{1}{6}} \] Simplifying this further, we find that: \[ m = 12 \] Thus, the correct answer is \(12\).