The «natural logarithm» is a special function. In this article you will learn how it is defined, what properties it has and how you can derive the function.
Just like the general logarithm function, you can also use the ln function to solve a specific equation. The following applies:
The number is the number for which the following equation applies:
In the following you will find application examples.
The following equation is given:
To such equations to solve and determine what e must be raised to the power to get 10 here the logarithm. This is noted as follows:
Now give the expression into the calculatoryou get the following solution:
With the natural logarithm you can ask yourself the following question: «What number do I have to raise to the power to get the solution?»
Because from the equation follows, you can look at the two Laws of the natural logarithm notice:
Rules and laws of the natural logarithmic function
When calculating with the natural logarithm, there are different calculation rules:
The graph of the natural logarithm function
The following figure shows the graph of a natural logarithmic function.
As a reminder, in order to find the zeros of a function, it must be equated.
If you now apply the inverse function, you get the following expression:
If you solve this equation completely, you get the following zero:
So owns the natural logarithm function the root, just like any general logarithmic function with base.
Monotonicity of the natural logarithmic function
the monotony the general logarithm function depends on the base.
In memory of:
- For the general logarithmic function is strictly increasing.
- For the general logarithmic function is strictly decreasing.
The ln function is strictly increasingi.ea at the natural logarithm function the base is.