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Find p in terms of q if \(\log_{3} p + 3\log_{3} q = 3\)

Mathematics
JAMB 1989

Find p in terms of q if \(\log_{3} p + 3\log_{3} q = 3\)

  • A. (\(\frac{3}{q}\))3
  • B. (\(\frac{q}{3}\))\(\frac{1}{3}\)
  • C. (\(\frac{q}{3}\))3
  • D. (\(\frac{3}{q}\))\(\frac{1}{3}\)
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Correct Answer: Option A
Explanation

\(\log_{3} p + 3\log_{3} q = 3\)

\(\log_{3} p + \log_{3} q^{3} = 3\)

\(\implies \log_{3} (pq^{3}) = 3\)

\(pq^{3} = 3^{3} = 27\)

\(\therefore p = \frac{27}{q^{3}}\)

= \((\frac{3}{q})^{3}\)


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