Solve this multiple-choice question and choose the correct option.

Concept / Approach Use change of base: log5512 = log10512 / log105. Step-by-step calculationlog10512 = log10(29) = 9 × 0.3010 = 2.709log105 = 1 − log102 = 1 − 0.3010 = 0.6990log5512 = 2.709 / 0.6990 = 3.876 (approx.) Verification53 = 125 < 512 < 625 = 54 ⇒ answer between 3 and 4, consistent.

Curioustab

Given log102 = 0.3010 and log103 = 0.4771, evaluate log5512.

Aptitude Logarithm Difficulty: Medium

Choose an option

A

3.700
B

3.876
C

3.909
D

4.000

Answer

Correct Answer: 3.876

Explanation

Concept / Approach

Use change of base: log₅512 = log₁₀512 / log₁₀5.

Step-by-step calculationlog₁₀512 = log₁₀(2⁹) = 9 × 0.3010 = 2.709log₁₀5 = 1 − log₁₀2 = 1 − 0.3010 = 0.6990log₅512 = 2.709 / 0.6990 = 3.876 (approx.)

Verification5³ = 125 < 512 < 625 = 5⁴ ⇒ answer between 3 and 4, consistent.

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Given log<sub>10</sub>2 = 0.3010 and log<sub>10</sub>3 = 0.4771, evaluate log<sub>5</sub>512.

Answer

Explanation