- #1

Monoxdifly

MHB

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- 0

A. \(\displaystyle \frac13\)

B. \(\displaystyle \frac12\)

C. 3

D. 5

E. 7

Since \(\displaystyle p,q,\frac1{8pq}\) is a geometric sequence, then:

\(\displaystyle \frac{q}{p}=\frac{\frac1{8pq}}q\)

\(\displaystyle \frac{q}{p}=\frac1{8pq^2}\)

\(\displaystyle q=\frac1{8q^2}\)

\(\displaystyle q^3=\frac18\)

\(\displaystyle q=\frac12\)

Also, since \(\displaystyle log_a18+log_ap=1\), then:

\(\displaystyle log_a18p=log_aa\)

18p = a

\(\displaystyle p=\frac{a}{18}\)

This is where the real problem starts. No matter how I substitute, either it will cancel out the a's or p's, or becoming a quadratic equation with no real roots. What should I do?