Evaluate log_6( log_5(15625) ).
Aptitude
Logarithm
Difficulty: Easy
Choose an option
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A1
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B2
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C3
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DNone of these
Answer
Correct Answer: 1
Explanation
Introduction / Context:This tests composition of logs with different bases. Simplify the inner logarithm first by recognizing perfect powers, then apply the outer logarithm.
Given Data / Assumptions:15625 is a power of 5.
Concept / Approach:Compute t = log_5(15625). Since 15625 = 5^6, t = 6. Then evaluate log_6(6) = 1.
Step-by-Step Solution:
15625 = 5^6 ⇒ log_5(15625) = 6log_6(6) = 1Why Other Options Are Wrong:2 or 3 result from misidentifying the power of 5 or misapplying the outer log.
Final Answer:1