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Question

Evaluate:
limx0log(2+x)log(2x)x

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Solution

limx0log(2+x)log(2x)x
=limx0log(2+x2x)x Adding and substracting 1,
=limx0log(1+2+x2x1)x
=limx0log(1+2x2x)(2x2x)×(2x2)
=limx0log[1+2x2x]2x2x×limx022x (limx0log(1+x)x=1)
=1×220=1.

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