3^2 log _35 = #160; 3^23^( log_35) #160; #160; #160; #160; #160; #160; #160; .... [∵ a^m+n=a^m.a^n] #160; =9 × 3^( 1 ...

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Theorems for Continuity

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Question

Evaluate : $3^{2 - {log}_{3} 5}$

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Solution

$3^{2 - {log}_{3} 5}$ = $3^{2} 3^{(- {log}_{3} 5)}$ .... $[∵ a^{m + n} = a^{m} . a^{n}]$
$= 9 \times 3^{(- 1) {log}_{3} 5}$
$= 9 \times 5^{- 1}$
$= \frac{9}{5} .$

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