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Solve the given equation \((\log_{3} x)^{2} - 6(\log_{3} x) ...

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

View answer & explanation

Correct answer is A

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

Let $\log_{3} x = a$ .

$a^{2} - 6a + 9 = 0$

$a^{2} - 3a - 3a + 9 = 0$

$a(a - 3) - 3(a - 3) = 0$

$(a - 3)(a - 3) = 0$

$\implies a = 3 (twice)$

$\log_{3} x = 3 \implies x = 3^{3} = 27$

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