\(\log_{6}\left(216\sqrt{6}\right)\) is
Show Hint
- 3
- \(\frac{3}{2}\)
- \(\frac{7}{2}\)
- None of these
The Correct Option is C
Solution and Explanation
\(216 = 6^3\) and \(\sqrt{6} = 6^{1/2}\), so \(216\sqrt{6} = 6^{3}\cdot 6^{1/2} = 6^{7/2}\).
Step 2: Take the logarithm:
\(\log_6\left(6^{7/2}\right) = \frac{7}{2}\).
Final Answer:
The correct option is (3): \(\frac{7}{2}\).
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