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If the sixth term in the expansion of 1 x 8 3 + x 2 log 10 ⁡ x 8 is 5600 , then the value of x is

Options

  1. A2
  2. B5
  3. C10
  4. D10

Correct answer

D. 10

Step-by-step solution

Note that for log 10 ⁡ x to be defined, x > 0 . We have, T 6 = T 5 + 1 = 8 C 5 1 x 8 3 8 - 5 x 2 log 10 ⁡ x 5 ⇒ 5600 = 8 × 7 × 6 3 × 2 1 x 8 x 10 log 10 ⁡ x 5 ⇒ 100 = x 2 log 10 ⁡ x 5 ⇒ 100 x 2 = log 10 ⁡ x 5 The curves y = 100 x 2 and y = log 10 ⁡ x 5 intersect in just one point 10,1 ⇒ x = 10

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