InterviewSolution
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InterviewSolution
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If the third term in the expansion of `(1/x+""_"x"(log)_(10 x))^5`is `1000 ,`then find `xdot`A. 100B. 10C. 1D. `1 sqrt(10)` |
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Answer» Correct Answer - a We have, `T_(3) = 1000` `rArr ""^(5)C_(2) ((1)/(x))^(5-2) (x^(log 10x))^(2) = 1000` `rArr x^(2) log_(10)^(x-3)= 100` `rArr 2 log_(10) x-3 = log_(x) 10^(2)` `rArr 2y - 3 = (2)/(y)` , where y `log_(10) x` `rArr 2y^(2) - 3y - 2 = 0` `rArr (2y+1)(y-2)= 0` `rArr y = 2 or y = 11//2` Now , ` y = 2 rArr log_(10) x = 2 rArr x = 10^(2) = 100` and , `y = - 1//2 rArr log_(10) x = - 1//2 rArr x = 10 ^(-1//2)` But , x `gt` 11, So, x = 100 |
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