Solve the given equation \((\log_{3} x)^{2} – 6(\log_{3} x) + 9 = 0\)

Explanation

\((\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0\)

Let \(\log_{3} x = a\).

\(a^{2} - 6a + 9 = 0\)

\(a^{2} - 3a - 3a + 9 = 0\)

\(a(a - 3) - 3(a - 3) = 0\)

\((a - 3)(a - 3) = 0\)

\(\implies a = 3 (twice)\)

\(\log_{3} x = 3 \implies x = 3^{3} = 27\)