Use natural logarithms
The most frequently used base for logarithms is e. Base e logarithms are important in calculus and some scientific applications; they are called natural logarithms. The base e logarithm, , has its own notation, .
Most values of can be found only using a calculator. The major exception is that, because the logarithm of 1 is always 0 in any base, . For other natural logarithms, we can use the key that can be found on most scientific calculators. We can also find the natural logarithm of any power of e using the inverse property of logarithms.
A General Note: Definition of the Natural Logarithm
A natural logarithm is a logarithm with base e. We write simply as . The natural logarithm of a positive number x satisfies the following definition.
For ,
We read as, "the logarithm with base e of x" or "the natural logarithm of x."
The logarithm y is the exponent to which e must be raised to get x.
Since the functions and are inverse functions, for all x and for .
How To: Given a natural logarithm with the form , evaluate it using a calculator.
- Press [LN].
- Enter the value given for x, followed by [ ) ].
- Press [ENTER].
Example 6: Evaluating a Natural Logarithm Using a Calculator
Evaluate to four decimal places using a calculator.
Solution
- Press [LN].
- Enter 500, followed by [ ) ].
- Press [ENTER].
Rounding to four decimal places,
Try It 6
Evaluate .
Solution