lim x→0(log(1/x)^log(1-x)

lim x→0(log(1/x)^log(1-x)
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1 Answer

The expression simplifies to:

-log(1-x)log(x).

log(1-x)→0 as x→0.

Take x=0.01 log₁₀(x)=-2 while log₁₀(1-x)=-0.004 approx, so log(1-x) is considerably smaller than log(x) and approaches 0 much faster than log(x)→-∞, so the limit is zero as x→0.

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