1988 AHSME Problems/Problem 26

Problem

Suppose that $p$ and $q$ are positive numbers for which

$\log_{9}(p) = \log_{12}(q) = \log_{16}(p+q)$

What is the value of $\frac{q}{p}$ ?

$\textbf{(A)}\ \frac{4}{3}\qquad \textbf{(B)}\ \frac{1+\sqrt{3}}{2}\qquad \textbf{(C)}\ \frac{8}{5}\qquad \textbf{(D)}\ \frac{1+\sqrt{5}}{2}\qquad \textbf{(E)}\ \frac{16}{9}$

Solution

1988 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 25	Followed by Problem 27
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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1988 AHSME Problems/Problem 26

Problem

Solution

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