Evaluate each of the following :
1) 3 $^{2 - l o g_{3} 4}$

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Solution

$3^{2 - {l o g}_{3} 4}$
$= 3^{2 - {l o g}_{3} 2^{2}}$
$= 3^{2 - 2 {l o g}_{3} 2}$
$= \frac{3^{2}}{3^{2 {l o g}_{3} 2}}$
$= \frac{3^{2}}{3^{{l o g}_{3} 4}}$
$= \frac{3^{2}}{4} (∵ a^{{l o g}_{a} b = b})$
$= \frac{9}{4}$

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