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If $x = \log_{3} 5, y = \log_{17} 25$ which one of the following is correct?

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$x < y$

$x = y$

$x > y$

$\frac{1}{y} < \frac{1}{x}$

answer is C.

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Detailed Solution

$y = \log_{17} 5^{2}$ , $x = \log_{3} 5$

$y = 2 \log_{17} 5$ , $\frac{1}{x} = \frac{1}{\log_{3} 5}$

$\frac{1}{y} = \frac{1}{2 \log_{5} 17}$ , $\log_{5} 3$

$\frac{1}{y} = \frac{1}{2} \log_{17} 5$ , $\frac{1}{x} = \frac{1}{2} \log_{5} \cdot 9$

Clearly, $\frac{1}{y} > \frac{1}{x}$

$\Rightarrow y < x$ (or) $x > y$ .

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