Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.9 Junior Find the answer

The product, $\log_a b \cdot \log_b a$ is equal to:

Pick one

Solution

$a^x=b$
$b^y=a$
${a^x}^y=a$
$xy=1$
$\log_a b\log_b a=1$
As a result, the answer should be $\boxed{\textbf{(A) }1}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.