If the third term in the expansion of 1x+xlog10⁡x5, x>1, is 1000, then value of x is

If the third term in the expansion of 1x+xlog10x5, x>1, is 1000, then value of x is

  1. A

    10

  2. B

    10

  3. C

    100

  4. D

    1010

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    Solution:

    T3=5C21x52xlog10 x2=100010x2log10 x3=1000(2t3)t=2 where t=log10 x2t23t2=0(2t+1)(t2)=0x=110  or  x=100

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