Logarithmic functions are another way of expressing exponential functions. Hence, all logarithmic functions are written with reference to an exponential base. Most graphing calculators support two logarithmic bases: the common base and the natural base. Common base logarithms use ten as a base, while natural base logarithms use Euler's number, or e, as a base. If you need to create log functions with other bases, you must use the change of base formula.

Navigate to the function display window. Most graphing calculators have a dedicated button for this. For example, on many Texas Instruments graphing calculators, you can press the "Y=" button in the upper left-hand corner of the button layout.

Enter either the common log or natural log of the quantity you wish to evaluate in a different base as the numerator of a fraction. Enter the corresponding common log or natural log of the base as the denominator. For example, for log base 4 of x, enter either "log(x)/log(4)" or "ln(x)/ln(4)."

Graph your function. Most graphing calculators have a dedicated graph view button. For example, on many Texas Instruments graphing calculators, you can press the "GRAPH" button in the upper right hand corner of the button layout. The graphs of both "log(x)/log(4)" and "ln(x)/ln(4)" will be identical to the graph of the log base 4 of x.

## Tips

• The logarithmic change of base formula states that the log base a of b equals the log base c of b divided by the log base c of a. This allows you to use your calculator's "log" and "ln" buttons to evaluate logarithms of any base.