calculus - Calculate the limit: $lim_{xtoinfty} sqrt[x]{3^x+7^x}$

Calculate the limit: $$\lim_{x\to\infty} \sqrt[x]{3^x+7^x}$$

I'm pretty much clueless on how to approach this. I've tried using the identity of $c^x = e^{x \cdot \ln(c)}$ but that led me to nothing. Also I've tried replacing $x$ with $t=\frac{1}{x}$ such that I would end up with $\lim_{t\to 0} (3^{1/t} + 7^{1/t})^{1/t}$ however I've reached yet again a dead end.

Any suggestions or even hints on what should I do next?

Answer

Note that

$$\sqrt[x]{3^x+7^x}=7\sqrt[x]{1+(3/7)^x}=7\cdot \large{e^{\frac{\log{1+(3/7)^x}}{x}}}\to7$$