The natural logarithm of a number is the logarithm to the base , where is the mathematical constant approximately equal to . It is usually written using the shorthand notation , instead of as you might expect . You can rewrite a natural logarithm in exponential form as follows:
On a scientific calculator, you can simply press followed by to get the answer: approximately .
The exponential form of the equation you're solving is
Solve the equation. Round to the nearest thousandth.
First, rewrite the equation in exponential form.
Use a calculator. (Most scientific calculators have a button which gives a good approximation for ; if yours doesn't have one, use .)
The usual properties of logarithms are also true for the natural logarithm.
The following property lets you simplify logarithms of a power:
Now use the property that the log of a product is equal to the sum of the logs.
The graph of the logarithmic function (shown in blue, below) looks similar to the graphs of related functions or (remember that if no base is written, the base of the logairthm is understood to be ).
The function has an asymptote at and an -intercept at . It passes through the points and .