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Difference between revisions of "1957 AHSME Problems/Problem 33"

(Created page with "==Problem== If <math>9^{x + 2} = 240 + 9^x</math>, then the value of <math>x</math> is: <math>\textbf{(A)}\ 0.1 \qquad \textbf{(B)}\ 0.2\qquad \textbf{(C)}\ 0.3\qquad \textb...")
 
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Latest revision as of 06:53, 26 July 2024

Problem

If $9^{x + 2} = 240 + 9^x$, then the value of $x$ is:

$\textbf{(A)}\ 0.1 \qquad \textbf{(B)}\ 0.2\qquad \textbf{(C)}\ 0.3\qquad \textbf{(D)}\ 0.4\qquad \textbf{(E)}\ 0.5$

Solution

$9^{x+2}$ can be rewritten as $9^x*9^2=9^x*81$, which means the equation can be rewritten as $81(9^x)=240+9^x$, or $80(9^x)=240$, or $9^x=3$. Therefore, $x=\boxed{\textbf{(E) }0.5}$.

See Also

1957 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 32 		Followed by
Problem 34
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All AHSME Problems and Solutions

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