If sum of the integral values of \( x \) satisfying the equation \(...

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If sum of the integral values of \( x \) satisfying the equation \( |x-1|^{\log ^{2} x-\log x^{2}}=|x-1|^{3} \) is \( \mathrm{N} \),
\( \mathrm{P} \) then find characteristic of logarithm of \( \mathrm{N} \) to the base 5 .

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