Question

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Answer 1

Question -

$find \: the \: value \: of \: x \: satisfying \\ ({ \sqrt{3} )}^{ - 4 + 2 log\sqrt{5} x} = \frac{1}{9}$

Solution -

${( \sqrt{3}) }^{ - 4 + 2 log \sqrt{5} x } = \frac{1}{9}$

${( \sqrt{3} )}^{ - 4 + 2log \sqrt{5}x } = {9}^{ - 1}$

${( \sqrt{3}) }^{ - 4 + 2log \sqrt{5} x} = 3 {}^{ - 2}$

${( \sqrt{3}) }^{ - 4 + 2log \sqrt{5}x } = ({ \sqrt{3}) }^{ - 4}$

By equating,

$- 4 + 2log \sqrt{5} x = - 4$

$2log \sqrt{5} x = 0$

$log \sqrt{5} x = 0$

Taking exponential of the above equation we will get -

$x = {( \sqrt{5} )}^{0}$

$x = 1$

Therefore the value of x is 1