CAT 2022 Slot 2 · Quant · Logarithms and Indices · medium

Solve for x: log₂x + log₄x = 6.

Single correct option

A. 8
B. 12
C. 16
D. 32

Show answer and solution

Answer: (C) 16

Convert log₄x to base 2: log₄x = log₂x / log₂4 = log₂x / 2. So the equation becomes log₂x + (log₂x)/2 = 6, i.e., (3/2)log₂x = 6, so log₂x = 4, giving x = 2⁴ = 16. Check: log₂16=4, log₄16=2, sum=6 ✓.

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