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Exponential Equation for x

CAT 2017 Slot 1 · Quantitative Ability · Medium · Exponents and Logarithms

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If 92x−1−81x−1=19449^{2x - 1} - 81^{x-1} = 1944, then xx is

  1. A.

    3

  2. B.

    94\frac{9}{4}

  3. C.

    49\frac{4}{9}

  4. D.

    13\frac{1}{3}

Answer

B

Explanation

92x−1=34x−29^{2x-1} = 3^{4x-2}, 81x−1=34x−481^{x-1} = 3^{4x-4}. 34x−2−34x−4=19443^{4x-2} - 3^{4x-4} = 1944 34x−4(32−1)=1944  ⟹  34x−4(8)=1944  ⟹  34x−4=243=353^{4x-4} (3^2 - 1) = 1944 \implies 3^{4x-4} (8) = 1944 \implies 3^{4x-4} = 243 = 3^5. 4x−4=5  ⟹  4x=9  ⟹  x=944x - 4 = 5 \implies 4x = 9 \implies x = \frac{9}{4}.

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