1962 AHSME Problems/Problem 4

Problem

If $8^x = 32$ , then $x$ equals:

$\textbf{(A)}\ 4\qquad\textbf{(B)}\ \frac{5}{3}\qquad\textbf{(C)}\ \frac{3}{2}\qquad\textbf{(D)}\ \frac{3}{5}\qquad\textbf{(E)}\ \frac{1}{4}$

Recognizing that $8=2^3$ , we know that $2^{3x}=32$ . Since $2^5=32$ , we have $2^{3x}=2^5$ . Therefore, $x=\dfrac{5}{3}$ .

So our answer is $\boxed{\textbf{(B)}\ \frac{5}{3}}$

1962 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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