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

Question

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

 f(x) grows faster than g(x). 

g(x) grows faster than f(x). 

f(x) and g(x) grow at the same rate. 

It cannot be determined.

Answer 1

f and g are inverses, i.e. the graphs are symmetric about the line y=x.

f is above the line and g is below it

The rate of increase depends on the interval in question: near x=1, the derivative of g(x) is quite steep (much bigger than 4^x), but as x increases toward ∞, the derivative of 4^x is bigger.