## What is a logarithmic function

The logarithmic function is the inverse of the exponential function. Where exponentiation tells you what the value of is, the logarithm tells you what value has if you know the value of .

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.