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If a is a perfect square, what is the value of a, given that ax = 1/8 and x = 3/2[(log_{2} a) - 3]?

Correct answer is '4'. Can you explain this answer?

Given, a^{x} = 1/8, x = 3/2[(log_{2} a) - 3]

⇒ a^{3/2[(log2 a) - 3]} = ⅛

Applying log to base 2 in both sides, we get,

3/2[(log_{2} a) - 3] log_{2} a = log_{2}(⅛)

⇒ 3/2[(log_{2} a) - 3] log_{2} a = -3

Let log_{2} a = x

⇒ (x - 3) x = -2

⇒ x^{2} -3x + 2 = 0

⇒ (x - 1)(x - 2) = 0

⇒ x = 1 or 2

⇒ log_{2 }a = 1 or log_{2} a = 2

⇒ a = 2 or a = 4

As given 'a' is a perfect square ⇒ a = 4

Hence, the correct answer is 4.

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If a is a perfect square, what is the value of a, given that ax = 1/8 and x = 3/2[(log2 a) - 3]?Correct answer is '4'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If a is a perfect square, what is the value of a, given that ax = 1/8 and x = 3/2[(log2 a) - 3]?Correct answer is '4'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a is a perfect square, what is the value of a, given that ax = 1/8 and x = 3/2[(log2 a) - 3]?Correct answer is '4'. Can you explain this answer?.

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Given, ax = 1/8, x = 3/2[(log2 a) - 3]⇒ a3/2[(log2 a) - 3] = ⅛Applying log to base 2 in both sides, we get,3/2[(log2 a) - 3] log2 a = log2(⅛)⇒ 3/2[(log2 a) - 3] log2 a = -3Let log2 a = x⇒ (x - 3) x = -2⇒ x2 -3x + 2 = 0⇒ (x - 1)(x - 2) = 0⇒ x = 1 or 2⇒ log2 a = 1 or log2 a = 2⇒ a = 2 or a = 4As given 'a' is a perfect square ⇒ a = 4Hence, the correct answer is 4.