How do you evaluate # x^(ln(7)/(1+ln(x)) # as x approaches infinity?

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Answer 1 · 2016-06-24T04:53:20

7

Let #y=x^(ln 7 /(1+ln x))#.

#ln y = ln 7/(1+ln x) ln x#

#lim x to oo# of # ln y#

# = ln 7 (lim x to oo# of #ln x/(1+ln x))#

Apply L'Hospital rule.

The limit of #ln y = ln 7 lim x to oo# of #(1/x)/(1/x)#

#=ln 7 (1)

So, #lim x to oo# of #y = 7#.