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The value of x for which the fourth term in the expansion of 5 2 5 log 5 ⁡ 4 x + 44 + 1 5 log 5 ⁡ 2 x - 1 + 7 3 8 is 336 can be equal to

Options

  1. A1 2
  2. B1
  3. C2
  4. D3

Correct answer

B. 1

Step-by-step solution

T 4 = C 8 3 5 1 5 log 5 ⁡ 4 x + 44 5 1 5 1 3 log 5 ⁡ 2 x - 1 + 7 3 = C 8 3 5 log 5 ⁡ 4 x + 44 5 log 5 ⁡ 2 x - 1 + 7 - 1 = C 8 3 × 4 x + 44 × 2 x - 1 + 7 - 1 Given, T 4 = 336 ⇒ 4 x + 44 2 x - 1 + 7 - 1 = 6 ⇒ 4 x + 44 = 3 ⋅ 2 x + 42 ⇒ 2 x 2 - 3 ⋅ 2 x + 2 = 0 ⇒ 2 x = 1,2 ⇒ x = 0 or 1

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