## Logarithms

We consider logarithms with three different bases:

base e (natural logarithms),
base 10, and
base b other than e or 10, where 0 < b and b 1.

Recall that the domain of a logarithm function consists of all real numbers x > 0.

In the examples below, the Exact/Approx mode is in AUTO.

Base e
 Simply use the LN key (located above the X key). For example, to calculate ln(17), press LN to get a decimal approximation

Base 10
The TI-89 does not have a logarithm base 10 key. However, one can use logarithm base 10 from the catalog. Press CATALOG to access the catalog. To navigate to log( , press L, then , then press the blue down arrow on the thumb pad, then press the blue down arrow 5 times to select log( . Press . Enter the number of interest, then press the right parenthesis.

For example, the screen displays the calculations for log(17). Notice that the TI-89 uses the change of base formula to convert logarithms base 10 to logarithms base e.

Other Bases
 For logarithmic bases other than e or 10, one must apply the change of base formula to convert to base e:

Hence, to determine log5(17), note that log5(17) = ln(17)/ln(5). Finally press to get a decimal approximation. Here, log5(17) 1.76037.