Find p in terms of q if \(\log_{3} p + 3\log_{3} q = 3\)
-
(\(\frac{3}{q}\))3
- (\(\frac{q}{3}\))\(\frac{1}{3}\)
- (\(\frac{q}{3}\))3
- (\(\frac{3}{q}\))\(\frac{1}{3}\)
The correct answer is: A
Explanation
\(\log_{3} p + 3\log_{3} q = 3\)
\(\log_{3} p + \log_{3} q^{3} = 3\)
\(\implies \log_{3} (pq^{3}) = 3\)
\(pq^{3} = 3^{3} = 27\)
\(\therefore p = \frac{27}{q^{3}}\)
= \((\frac{3}{q})^{3}\)