# Thread: Relative Rates of Growth

1. ## Relative Rates of Growth

Order the function from slowest-growing to fastest growing as x--> infinity. Show your work.

x^(6), e^(x), 6^(x), (ln(6))^(x)

I don't know how I would go about comparing 4 functions together.. also i'm having trouble evaluating

e^x to 6^x.. i keep getting an indeterminate form..

2. Originally Posted by AIYAH

e^x to 6^x.. i keep getting an indeterminate form..
Can't you say as

$6 > e$ then as $x\to\infty, 6^x > e^x$

3. Originally Posted by pickslides
Can't you say as

$6 > e$ then as $x\to\infty, 6^x > e^x$

Oh yes that is true.. now the next part of the question... hmm.

4. The next part? I'm not sure exactly what you mean?

$6 > e > \ln(6)$ then as $x\to\infty, 6^x > e^x > \ln(6)^x$

5. ohhh.. i can do that to the other problems too.
i get it now ^.^