If the 4 t h term in the expansion of x 1 log 10 ⁡ x + 1 + x 1 12 6 is 200 , then the value of x is (where, x 1 )

Question

If the 4 t h term in the expansion of x 1 log 10 ⁡ x + 1 + x 1 12 6 is 200 , then the value of x is (where, x > 1 ),

MARKS App · Accepted Answer

T 4 = C 3 6 x 1 log 10 x + 1 3 x 1 12 3 ⇒ 200 = 20 x 1 l o g 10 x + 1 3 2 x 1 4 ⇒ 10 = x 3 2 1 log 10 x + 1 + 1 4 ⇒ 1 t = 3 2 1 t + 1 + 1 4 ….. [Take t = log 10 x ] ⇒ t 2 + 3 t - 4 = 0 ⇒ t - 1 t + 4 = 0 ⇒ t = 1 or t = - 4 ⇒ log 10 x = 1 or log 10 x = - 4 ⇒ x = 10 … [as x > 1 ]

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