Trouble Solving: The Limit of x→∞ ln(√x + 5)/ln(x)

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SUMMARY

The limit as x approaches positive infinity of ln(√x + 5)/ln(x) presents an indeterminate form. To resolve this, L'Hôpital's Rule is applicable, allowing for the differentiation of the numerator and denominator. The discussion confirms that evaluating the limits separately leads to a clearer understanding of the behavior of the function as x approaches infinity. The final result can be computed using a calculator for verification.

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The problem is

The limit as x approaches pos infinity ln(square root of x + 5) divided by ln(x)

In the numerator only x is under the square root. I'm having trouble getting to this answer. If someone can take a look I would really appreciate it.

I have the answer because it can be done on a calculator. Just I'm not sure how to get there.
 
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Well what is lim x-> infty ln(sqrt(x)+5) and lim x-> ln(x)?
 
try evaluating the limit as my friend above me pointed out, you will get an indeterminate form. Fortunately l'hospital's rule can be used to deal with such limits.
 

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