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
(\(\frac{3}{q}\))\(\frac{1}{3}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\log_{3} p + 3\log_{3} q = 3\)
\(\log_{3} p + \log_{3} q^{3} = 3\)
\(\implies \log_{3} (pq^{3}) = 3\)
\(pq^{3} = 3^{3} = 27\)
\(\therefore p = \frac{27}{q^{3}}\)
= \((\frac{3}{q})^{3}\)
Source: Myschool Past Questions Archive (Record #31504)