Help with Calc please!

Question

Compare the growth rate of the functions f(x) = log₄(x) and g(x) = 4^x.

Options:

1)	f(x) grows faster than g(x).
2)	g(x) grows faster than f(x).
3)	f(x) and g(x) grow at the same rate.
4)	It cannot be determined.

Answer 1

4^X grows faster, but if you are unsure, you should graph the 2 equations.

Ooops!

I made a tacit assumption that the question referred to rate of growth as x -> ∞ and with that assumption my answer is correct.

However. on the interval (0,1) the rate of growth of the log function is (much) faster than 4^x!