How are exponential functions related to logarithmic functions?Model that with an example.
Accepted Solution
A:
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: [tex] {e}^{y} = x[/tex] 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: [tex]{e}^{y} = x[/tex] switch the x and y, then solve for y: [tex] {e}^{x} = y[/tex] So the exponential function is the inverse of the logarithmic one, f(x) = ln x