Calculus: Early Transcendentals, Chapter 1, Review Exercises, Section Review Exercises, Problem 28

Graph the three functions $y = x^a, y = a^x,$ and $y = \log_a x$ on the same screen
for two or three values of $a > 1$. For large values of $x$, which of these function has
the largest values and which has the smallest values?







We can see from the graphs that the graph of $y = a^x$ is more steep than the other. So,
for large values of $x$, the fraction $y = a^x$ has the largest values. On the other hand, for small values
of $x$, the fraction $y = \log ax$ has the smallest values.