What is a logarithmic function

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

A logarithmic function describes a function equation for a base equation. Often when we talk of logarithmic functions, we mean the natural logarithm equation which has base equation (Euler’s number). In this case equation. First, we have a look at what this function looks like when plotted:


We see that the graph intersects the x-axis at equation. This is the case for any logarithmic function regardless of the base. Knowing the point equation 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 equation. Have a look at the following graph, where the red function is equation and the purple function is equation and see how they are mirrored at the black line which is equation.


For more information about the logarithm and how to change its base, read the article on logarithms.