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AP EAMCET202022 Sep 2020Evening ShiftMathematicsLimitsActual

If _ x 3 ( x^n-3^n x-3 )=108 and n N , then the value of ' n ' is

Options

  1. A3
  2. B6
  3. C5
  4. D4

Correct answer

D. 4

Step-by-step solution

_ x 3 x^n-3^n x-3 =108 LHS is in from, so apply L-Hospital rule aligned _ x 3 n x^ n-1 -0 1-0 & =108 _ x 3 n x^ n-1 & =108 n 3^ n-1 & =108 n 3^n 3 & =108 aligned aligned & n 3^n=3 108 & n 3^n=3 (3^3 4 ) & n 3^n=4 3^4 aligned On comparison n=4 Hence, option (4) is correct.

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