Graphs of Logarithmic Functions The logarithmic function is the inverse function to the exponential function. The logarithmic function is defined as f (x) = log a (x) where a, x ∈ R + and a ≠ 1. The ...

The second way to graph the inverse function is algebraic. Start with the original equation’s function, swap x and y, and then solve. For example: f (x) = 5x +10 (original function of x) ...

These studies collectively underscore a trend towards more unified frameworks that address both the forward control challenges and the inverse identification problems in an integrated manner [5].