Question

How are exponential functions related to logarithmic functions? Model that with an example.

Answer 1

Exponential functions are related to logarithmic functions in that they are inverse functions. Exponential functions move quickly up towards a [y] infinity, bounded by a vertical asymptote (aka limit), whereas logarithmic functions start quick but then taper out towards an [x] infinity, bounded by a horizontal asymptote (aka limit).
If we use the natural logarithm (ln) as an example, the constant "e" is the base of ln, such that:
ln(x) = y, which is really stating that the base (assumed "e" even though not shown), that:
${e}^{y} = x$
if we try to solve for y in this form it's nearly impossible, that's why we stick with ln(x) = y
but to find the inverse of the form:
${e}^{y} = x$
switch the x and y, then solve for y:
${e}^{x} = y$
So the exponential function is the inverse of the logarithmic one, f(x) = ln x