-\ln \left(1-x\right)+x\ln \left(1-x\right)+1-x

asked by guest
on Sep 19, 2024 at 5:34 pm



You asked:

Evaluate the expression: \(-\ln\left( 1 - x \right) + x \cdot \ln\left( 1 - x \right) + 1 - x\)

MathBot Answer:

Evaluated



\(\displaystyle -\ln\left( 1 - x \right) + x \cdot \ln\left( 1 - x \right) + 1 - x = x \log{\left(1 - x \right)} - x - \log{\left(1 - x \right)} + 1 \)

Factored

\[-\ln\left( 1 - x \right) + x \cdot \ln\left( 1 - x \right) + 1 - x = \left(x - 1\right) \left(\log{\left(1 - x \right)} - 1\right)\]

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