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Difference between revisions of "1962 AHSME Problems/Problem 4"

(Created page with "==Problem== If <math>8^x = 32</math>, then x equals: <math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ \frac{5}{3}\qquad\textbf{(C)}\ \frac{3}{2}\qquad\textbf{(D)}\ \frac{3}{5}\qquad\...")
 
(→‎Solution)
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==Solution==
 
==Solution==
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Recognizing that <math>8=2^3</math>, we know that <math>2^{3x}=32</math>. Since <math>2^5=32</math>, we have <math>2^{3x}=2^5</math>. Therefore, <math>x=\dfrac{5}{3}</math>.
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So our answer is <math>\boxed{\textbf{(B)}\ \frac{5}{3}}</math>

Revision as of 00:15, 10 November 2013

Problem

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

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

Solution

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 $\boxed{\textbf{(B)}\ \frac{5}{3}}$

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