What is the Limit of (4^x + 7^x)^(1/x) as x Approaches Infinity?

[The_Journey]

Homework Statement

lim n->infinity (4^x + 7^x)^(1/x)

Homework Equations

Not applicable (?)

The Attempt at a Solution

Tried taking "plugging" infinity for n but I keep getting 1, is this right?

Seems too easy to be just 1?

Thank you.

 

[olivermsun]

1 isn't right.

Look at the thing being raised to the power 1/x. Which one will dominate as x gets large?

 

[flyingpig]

Take the natural logarithm

 

[The_Journey]

@olivermsun: The 4^x and 7^x will be bigger, but I am lost at the next step.

@flyingpig: Am I allowed to take the natural log of the function? Won't that change the limit?

 

[Sethric]

I think olivermsun is saying that one of those two terms will dominate as x gets larger.

 

[Delta2]

Find the limit of lnf(x), and then you can find the original limit as e^{limlnf(x)}. Seems 7 to be the final answer.

 

[The_Journey]

Ah thank you very much Delta, totally forgot about that part :)