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  4. displaystyle limx → 1 loge(ex(x-1)-ex(1-x))-loge(4x(x-1)) is equal to :

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Q. $\displaystyle \lim_{x \to 1}$$\left\{log_{e}\left(e^{x\left(x-1\right)}-e^{x\left(1-x\right)}\right)-log_{e}\left(4x\left(x-1\right)\right)\right\}$ is equal to :

JEE MainJEE Main 2020Limits and Derivatives

Solution:

Correct answer is (d) $-\,log_e\,2$