Question

log a base 5 × log x base a = 2,find x​

Answer 1

Solution:

$log_{a}5\times log_{x}a = 2$

We know that,

$\blue{ \because log_{a}m\times log_{n}a= log_{n}m}$

$\implies log_{x}5 = 2$

$\boxed{ \pink{ \because log_{x}m = N \implies m = x^{N}}}$

$\implies 5 = x^{2}$

$\implies x = \sqrt{5}$

Therefore.,

$\red{ Value \: of \: x } \green { = \sqrt{5}}$

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