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Welcome to our Math lesson on The Natural Logarithm Function and its Graph, this is the sixth lesson of our suite of math lessons covering the topic of Natural Logarithm Function and Its Graph, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
The natural logarithm function is a special type of logarithmic function. The simplest form of the natural logarithmic function is
Other functions that contain the natural logarithm are
Obviously, we give some values to the independent variable x and by substituting them in the function's formula we then calculate the corresponding y-values, which represent the dependent variable.
The graph of 'ln' function is similar to that of the other logarithmic functions discussed in the previous tutorial.
The graph of the simplest version of the 'ln' function is shown in the figure below.
As you see, the x-intercept is at the point x = 1, where y = 0. Indeed,
On the other hand, you can see that the value y = 1 corresponds to a point between x = 2.5 and x = 3 (where it should be), as
The natural logarithmic function is the inverse of the natural exponential function, in the sense that the graphs of these two functions mirror each other according the line y = x, which acts as a symmetry line. We discuss this more extensively in chapter 28 where we cover reflections and figures mirroring, for now we can state that such a situation is observed when one figure is folded according to the line of symmetry to give the other figure.
Both graphs of the above functions are provided in the same figure here below, as well as the line of symmetry y = x.
It is evident that if we fold the figure according to the line y = x, the two graphs fit perfectly with each other.
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