Question

limit as x approaches infinity of (x)/log_2(3^x))

Answer 1

\[ \lim_{x\to \infty} \frac{x}{\log _2\left(3^x\right)}\]

Answer 2

right

Answer 3

I am trying to compare asymptotic behavior

Answer 4

so I know this is an infinity over infinity case, how would I find the derivative of the denominator?

Answer 5

You can either use the "rules" for log deriv or say to hell with the rules!

Actually no, use the other rules... \[\large \log a^x = x \log a\]easy now huh ;)

Answer 6

\[\lim_{x\to \infty} \frac{x}{\log _2\left(3^x\right)} = \lim_{x\to \infty} \frac{x}{x\log _2\left(3\right)}\]

Answer 7

\[\frac{ 1 }{ 3 \ln(2) }\]

Answer 8

https://cdn.meme.am/instances/500x/55941579.jpg