JEE Advanced · MathematicsMedium

$The value of the expression lo g_{2} (lo g_{3} (81)) is:$

A. $1$
B. $2$
C. $3$
D. $4$

Show correct answer & step-by-step solution

Correct answer: B — $2$

Solution

$Evaluate the inner term lo g_{3} (81) .$
$Since 81 = 3^{4}, lo g_{3} (81) = 4 .$
$Now evaluate lo g_{2} (4) .$
$Since 4 = 2^{2}, lo g_{2} (4) = 2 .$
$Hence the answer is (B).$

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