If $log x / 2 = log y / 3,$ find the value of $y^{4} / x^{6} .$

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Solution

Given:
$log x / 2 = log y / 3$
Let us simplify the given expression,By cross multiplying we ge
$3 log x = 2 log y$
$log x^{3} = log y^{2}$
So, $x^{3} = y^{2}$
now square on both sides, we get
$(x^{3})^{2} = (y^{2})^{2}$
$x^{6} = y^{4}$
$y^{4} / x^{6} = 1$

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