Which of the following functions grow faster then e^x as x approaches infinity?
x^4
ln(x)
e^(-x)
3^x
.5*e^x
Another reason as to why...
$\displaystyle 3^x > e^x$
Same exponent, but the left side has a larger base hence a larger outcome, and to connect this to TPH's explanation..
$\displaystyle ln|3|x > x$
$\displaystyle x \ne 0$ <- this follows because at zero the functions are equal
$\displaystyle ln|3| > 1$