Limit as x approaches infinity of ln(x)⋅ln(1−e−x):
limx→∞ln(x)⋅ln(1−e−x)
The only thing I can think to do is rewrite the ln(x) on the bottom as (lnx)−1 and use L’Hôpital’s rule, but I’ve done two iterations now and it keeps getting back to the 0/0 or infinity*0 indeterminate case. Any help on how to proceed will be much appreciated! Thanks
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