1953 AHSME Problems/Problem 5

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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 1

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

Solution 2

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


See Also

1953 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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