1957 AHSME Problems/Problem 28

Problem

If $a$ and $b$ are positive and $a\not= 1,\,b\not= 1$ , then the value of $b^{\log_b{a}}$ is:

$\textbf{(A)}\ \text{dependent upon }{b} \qquad \textbf{(B)}\ \text{dependent upon }{a}\qquad \textbf{(C)}\ \text{dependent upon }{a}\text{ and }{b}\qquad\textbf{(D)}\ \text{zero}\qquad\textbf{(E)}\ \text{one}$

Solution

By the fact that logarithms are the inverse of exponentiation, it is clear that $b^{log_b{a}}=a$ , so our answer is $\boxed{\textbf{(B)}\text{ dependent upon }a}$ .

1957 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 27	Followed by Problem 29
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1957 AHSME Problems/Problem 28

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