1953 AHSME Problems/Problem 39

Problem

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

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ a \qquad \textbf{(C)}\ b \qquad \textbf{(D)}\ ab \qquad \textbf{(E)}\ \text{none of these}$

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

1953 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 38	Followed by Problem 40
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