Basic Mathematics & Logarithm
Logarithm Properties
Grade None
Question:
<p>(C) Evaluate <span class="math">\(\frac{2\log 6}{\log 12 + \log 3}\)</span></p>
<p>(p) positive integer</p>
<p>(q) negative integer</p>
<p>(r) rational but not integer</p>
<p>(s) [incomplete in source]</p>
Step-by-Step Solution
Key Concept: Use logarithm product rule in denominator and power rule to simplify.
<p><strong>Step 1:</strong> Simplify the denominator: \(\log 12 + \log 3 = \log(12 \times 3) = \log 36\)</p><p><strong>Step 2:</strong> The expression becomes \(\frac{2\log 6}{\log 36}\)</p><p><strong>Step 3:</strong> Note that \(36 = 6^2\), so \(\log 36 = \log(6^2) = 2\log 6\)</p><p><strong>Step 4:</strong> Therefore, \(\frac{2\log 6}{2\log 6} = 1\)</p><p>∴ Answer is (p) positive integer.</p>
Correct Answer: r