InterviewSolution
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InterviewSolution
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Solve:` 27^(log_(3)root(3)(x^(2)-3x+1) )=(log_(2)(x-1))/(|log_(2)(x-1)|)`. |
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Answer» Correct Answer - x = 3 We have `27^(log_(3)root(3)(x^(2)-3x+1) )=(log_(2)(x-1))/(|log_(2) (x-1)|)` We must have `x-1 gt 0 and x - 1 ne 1` ` :. X gt and x ne 2` If ` 1 lt x lt 2, log_(2) (x-1) lt 0` `:. (log_(2)(x-1))/(|log_(2)(x-1)|) =- 1` This is not possible as L.H.S. ` gt 0` always. If ` x gt 2," then "(log_(2)(x-1))/(|log_(2)(x-1)|) = 1` `:." Equation reduces to "27^(log_(3)root(3)(x^(2)-3x+1))=1` `:gt x^(2)- 3x+1 = 1` ` rArr x = 0, 3," but "x ne 0` ` :. x = 3` is the only solution. |
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