1957 AHSME Problems/Problem 33

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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 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 32
Followed by
Problem 34
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