1958 AHSME Problems/Problem 25

Problem

If $\log_{k}{x}\cdot \log_{5}{k} = 3$, then $x$ equals:

$\textbf{(A)}\ k^6\qquad  \textbf{(B)}\ 5k^3\qquad  \textbf{(C)}\ k^3\qquad  \textbf{(D)}\ 243\qquad  \textbf{(E)}\ 125$

Solution

125. Rearrange the equation into \[\log_{5}{k}\cdot\log_{k}{x} = 3\] which is just \[\log_{5}{x} = 3\] and x is 125.

See Also

1958 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 24
Followed by
Problem 26
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