The value of `((log)_2 24)/((log)_(96)2)-((log)_2 192)/((log)_(12)2)` is 3 (b) 0 (c) 2 (d) 1

Explanation

To solve the expression \(\frac{\log_2 24}{\log_{96} 2} - \frac{\log_2 192}{\log_{12} 2}\), we can use the change of base formula for logarithms, which states that \(\log_a b = \frac{\log_c b}{\log_c a}\). We will use base 2 for our calculations.

### Step 1: Rewrite the logarithms using the change of base formula
Using the change of base formula, we can rewrite the expression as:
\[ \frac{\log_2 24}{\log_{96} 2} = \frac{\log_2 24}{\frac{\log_2 2}{\log_2 96}} = \frac{\log_2 24 \cdot \log_2 96}{\log_2 2} \]
Since \(\log_2 2 = 1\), this simplifies to:
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