If x = {log ₃}5,,,,y = {log _{17}}25, which one of following is correct

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Basic of Logarithms

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If $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct

A

$x < y$

B

$x = y$

C

$x > y$

D

None of these

Solution

(c) $y = {\log _{17}}25 = 2{\log _{17}}5$;

$\therefore {1 \over y} = {1 \over 2}{\log _5}17$

${1 \over x} = {\log _5}3 = {1 \over 2}{\log _5}9$.

Clearly, ${1 \over y} > {1 \over x}$; $\therefore x > y$

Standard 11

Mathematics

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