Solve the given equation \((\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0\)
A
27
B
9
C
\(\frac{1}{27}\)
D
18
E
81
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\((\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0\)
Let \(\log_{3} x = a\).
\(a^{2} - 6a + 9 = 0\)
\(a^{2} - 3a - 3a + 9 = 0\)
\(a(a - 3) - 3(a - 3) = 0\)
\((a - 3)(a - 3) = 0\)
\(\implies a = 3 (twice)\)
\(\log_{3} x = 3 \implies x = 3^{3} = 27\)
Source: Myschool Past Questions Archive (Record #32603)