If p^x = q, which logarithmic relation is correct?

Difficulty: Easy

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

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