1959 AHSME Problems/Problem 45
Problem
If 
, then 
equals:
Solution
From the properties of logarithms, we can simplify the equation and solve for :
\begin{align*}
(\log_3 x)(\log_x 2x)(\log_{2x} y) &= \log_{x}x^2 \\
(\log_3 2x)(\log_{2x} y) &= 2\log_x x \\
\log_3 y &= 2 \\
y &= 3^2 \\
y &= 9
\end{align*}
Thus, our answer is 
.
See also
| 1959 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 44 |
Followed by Problem 46 | |
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| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
