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1953 AHSME Problems/Problem 5

Revision as of 10:56, 7 June 2016 by Katzrockso (talk | contribs) (Created page with "==Problem 5== If <math>\log_6 x=2.5</math>, the value of <math>x</math> is: <math>\textbf{(A)}\ 90 \qquad \textbf{(B)}\ 36 \qquad \textbf{(C)}\ 36\sqrt{6} \qquad \textbf{(D...")
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Problem 5

If $\log_6 x=2.5$, the value of $x$ is:

$\textbf{(A)}\ 90 \qquad \textbf{(B)}\ 36 \qquad \textbf{(C)}\ 36\sqrt{6} \qquad \textbf{(D)}\ 0.5 \qquad \textbf{(E)}\ \text{none of these}$

Solution

$\log_6 x=\frac{5}{2}\implies 2\log_6 x=5\implies \log_6 x^2=5\implies x^2=6^5\implies x=36\sqrt{6}$, $\fbox{C}$

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