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1. $\log 5 (\sqrt[3]{5}) (\sqrt{5}) =$

Answer: Option C

Explanation:

\log_{5} (\sqrt[3]{5}) (\sqrt{5}) = \log_{5} (5^{\frac{1}{3}} . 5^{\frac{1}{2}}) = \log_{5} (5^{\frac{1}{3} + \frac{1}{2}}) = \log_{5} (5^{\frac{2 + 3}{6}}) = \log_{5} 5^{\frac{5}{6}} = \frac{5}{6} \log_{5} 5 = \frac{5}{6} \times 1 = \frac{5}{6}

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