What is a logarithmic function
A logarithmic function describes a function for a base . Often when we talk of logarithmic functions, we mean the natural logarithm which has base (Euler’s number). In this case . First, we have a look at what this function looks like when plotted:
We see that the graph intersects the x-axis at . This is the case for any logarithmic function regardless of the base. Knowing the point is useful when plotting a log function. Because the log function is the inverse of the exponentiation function, we can see that they are mirrored at the line . Have a look at the following graph, where the red function is and the purple function is and see how they are mirrored at the black line which is .
For more information about the logarithm and how to change its base, read the article on logarithms.