Evaluate: $3^{2 - {log}_{3} 4}$ .

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Solution

Solution-
$= 3^{2 - {log}_{3} 4} \to 2 = {log}_{3} 9$
$= 3^{{log}_{3} 9 - {log}_{3} 4} \to {log}_{a} - {log}_{b} = log (\frac{a}{b})$ .
$= 3^{{log}_{3} ⎛ ⎝ \frac{9}{4} ⎞ ⎠} . \to a^{{log}_{b} c} = c^{{log}_{b} a}$ .
$= \frac{9}{4}$

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