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If f(x) = x(1- log x), where c > 0, show that (a - b) log c = b(1 - log b) - a(1 - log a), where 0 < a < c < b.

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Best answer

Given: f(x) = x(1 - log x)

Since the function is continuous as well as differentiable

So, there exists c such that

(b - a) log c = b(1 - log b) - a(1 - log a)

Hence proved.

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