Compute (log_5 3) × (log_3 625).
Aptitude
Logarithm
Difficulty: Easy
Choose an option
-
A1
-
B2
-
C3
-
D4
Answer
Correct Answer: 4
Explanation
Introduction / Context:The product log_a b · log_b c equals log_a c by cancellation of the intermediate base. Apply that here with a = 5, b = 3, c = 625.
Given Data / Assumptions:625 = 5^4.
Concept / Approach:(log_5 3)(log_3 625) = log_5 625 = 4.
Step-by-Step Solution:
(log_5 3)(log_3 625) = (ln 3/ln 5)(ln 625/ln 3) = ln 625/ln 5 = log_5 625Since 625 = 5^4 ⇒ log_5 625 = 4Final Answer:4