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1. $\log_{7} (\sqrt[5]{7}, \sqrt{7}) - \log_{3} (\sqrt[3]{3}) + \log_{4} 2$

Answer: Option C

Explanation:

\log_{7} (\sqrt[5]{7} . \sqrt{7}) - \log_{3} \sqrt[3]{3} + \log_{4} 2 = \log_{7} 7^{\frac{1}{5}} - \log_{3} 3^{\frac{1}{3}} + \log_{4} 4^{\frac{1}{2}} = \log_{7} 7^{\frac{2 + 5}{10}} - \frac{1}{3} \log_{3} 3 + \frac{1}{2} \log_{4} 4 = \frac{7}{10} - \frac{1}{3} + \frac{1}{2} = \frac{21 - 10 + 15}{30} = \frac{26}{30} = \frac{13}{15} (A n s .)

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