If p^x = q, which logarithmic relation is correct?
Aptitude
Logarithm
Difficulty: Easy
Choose an option
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Alog_p x = q
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Blog_x q = p
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Clog_p q = x
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Dlog_q p = x
Answer
Correct Answer: log_p q = x
Explanation
Introduction / Context:Exponentials and logarithms are inverses. Translating p^x = q into a logarithmic statement tests understanding of this inverse relationship.
Given Data / Assumptions:p > 0, p ≠ 1, q > 0; p^x = q.
Concept / Approach:By definition, log base p of q equals the exponent x that raises p to q.
Step-by-Step Solution:
p^x = q ⇔ x = log_p(q)Why Other Options Are Wrong:They mismatch positions of base/argument or set the log equal to the base rather than the exponent.
Final Answer:log_p q = x