If $2 log x + 3 log y = log 4$ then $x^{2} y^{3} =$ ?

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Solution

$2 log x + 3 log y = log 4$
$∴ log x^{2} + log y^{3} = log 4$ ....( $log a^{b} = b log a$ )
$∴ log x^{2} . y^{3} = log 4$ ....( $log a . b = log a + log b$ )
$∴ x^{2} . y^{3} = 4$

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