standard_description: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
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