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Basic of Logarithms
medium
If ${\log _k}x.\,{\log _5}k = {\log _x}5,k \ne 1,k > 0,$ then $x$ is equal to
A
$k$
B
${1 \over 5}$
C
$5$
D
$(b)$ and $(c)$ both
Solution
(d) ${\log _k}x.{\log _5}k = {\log _x}5$ $ \Rightarrow $ ${\log _5}x = {\log _x}5$
$ \Rightarrow $ ${\log _x}5 = {1 \over {{{\log }_x}5}}$ $\Rightarrow $ $1 = – 2B = 0$
$ \Rightarrow $ ${\log _x}5 = \pm 1$
$ \Rightarrow $ ${x^{ \pm \,1}} = 5$ $ \Rightarrow $ $x = 5,\,{1 \over 5}$.
Standard 11
Mathematics
