standard_description: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
problem_activity: Task
Below is a picture of the functions $f(x) = \log_b{x}$ and $g(x) = b^x$. In the application below, the base b varies between 1 and 2 (by hundredths) and pressing the "play" button will run through all possible values of b.
For which values of $b$ do the two graphs appear not to meet?
For which values of $b$ do the two graphs appear to meet in two points?
Check by evaluating the functions $f$ and $g$ that the two graphs meet at $x=e$ when $b = e^{\frac{1}{e}}$.


aligns: no