If-log-11-3p-log-13-q-6p-log-143-q-2-find-p-q-

Question Number 182632 by cortano1 last updated on 12/Dec/22

If \log_{11} (3 p) = \log_{13} (q + 6 p) = \log_{143} (q^{2})

find \frac{p}{q} .

Answered by manxsol last updated on 12/Dec/22

3 p = 11^{k}

q + 6 p = 13^{k}

q^{2} = 11^{k} . 13^{k}

\dots \dots \dots \dots \dots . .

q^{2} = 3 p (q + 6 p)

q^{2} = 3 p q + 18 p^{2}

1 = 3 (\frac{p}{q}) + 18 {(\frac{p}{q})}^{2} \frac{p}{q} = x

18 x^{2} + 3 x - 1 = 0

(6 x - 1) (3 x + 1) = 0

\frac{p}{q} = \frac{1}{6}

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