Special Bases

There are two bases that are usually featured on scientific and graphing calculators. These bases are 10 and e, the number introduced in the section on exponential functions.

Notation

is equivalent to and is some times called the common logarithm .

is equivalent to and is called the natural logarithm .

Example 1

Each of the following includes a calculation of a logarithm along with its justification.

since

since

since

since

Example 2

Use a calculator to find , , , and

Solution .

To check these last two calculate and Both results should be close to 0.5.

It is important to note that