Question Bank • QB_EXP_GA_ALG_003 MCQ • 1 Mark

Section 8: General Aptitude

Quantitative: Algebra, Functions & Progressions

Subtopic: Logarithm base change identity

Question Statement:

If $\log_2 (x) + \log_4 (x) = 6$, the value of $x$ is:

Options:

  • (A) $16$
  • (B) $64$
  • (C) $8$
  • (D) $32$

Answer Key:

A

Step-by-Step Solution & Explanation

Using base change formula $\log_4 (x) = \frac{\log_2 (x)}{\log_2 (4)} = \frac{1}{2} \log_2 (x)$: $\log_2 (x) + \frac{1}{2} \log_2 (x) = \frac{3}{2} \log_2 (x) = 6$ $\log_2 (x) = 6 \times \frac{2}{3} = 4 \implies x = 2^4 = 16$.
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