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

Question

15920 views around the world

You can reuse this answer
Creative Commons License

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 $y = 7$ .

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