Solve this following

Question:

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

Solution:

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