If log_10(10x) = 2.7532, find log_10(10000x).
Aptitude
Logarithm
Difficulty: Easy
Choose an option
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A4.7532
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B5.7532
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C3 × 2.7532
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DNone of these
Answer
Correct Answer: 5.7532
Explanation
Introduction / Context:Multiplying a positive number by a power of 10 increases its common logarithm by the exponent (the characteristic). This is standard in mantissa–characteristic operations.
Given Data / Assumptions:log_10(10x) = 2.7532 ⇒ log_10(x) = 1.7532.
Concept / Approach:Compute log_10(10000x) = log_10(x) + 4 because 10000 = 10^4.
Step-by-Step Solution:
log_10(x) = 2.7532 − 1 = 1.7532log_10(10000x) = 1.7532 + 4 = 5.7532Final Answer:5.7532