[30] If log_{a}b =\dfrac{1}{2}, log_{b}c =\dfrac{1}{3}\:and\: log

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If $log_{a}b$ =$\dfrac{1}{2}, log_{b}c$ =$\dfrac{1}{3}\:and\: log_{c}a$ =$\dfrac{k}{5}$, the value of k is

Explanation:

$log_{a}b$ =$\dfrac{log\:b}{log\:a}, log_{b}c$ =$\dfrac{log\:c}{log\:b}, log_{c}a$ =$\dfrac{log\:a}{log\:c}$

$log_{a}b \times log_{b}c \times log_{c}a$ =$\dfrac{log\:b}{log\:a}\times\dfrac{log\:c}{log\:b}\times\dfrac{log\:a}{log\:c}$=$\dfrac{1}{2}\times\dfrac{1}{3}\times\dfrac{k}{5}$

=>1=$\dfrac{k}{30}$

=>k = 30

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