Natural logarithm

Returns the natural logarithm of the given expression.

The natural logarithm is the logarithm with base e.

Syntax

ln(Expression)

Examples

Calculating logarithms

Logarithms can be entered as log(number, base) or using the logarithm template log. If the base is omitted, the logarithm is interpreted as base 10. The natural logarithm is written with ln(). The number e (Euler's number) can be typed as @e, or selected from the pi menu or symbol palette.

Simplifying logarithmic expressions

Many logarithmic expressions can be simplified simply by pressing Enter. If the expressions include variables, it is often necessary to define a domain to allow simplification. You can also try using expand and factor. These tools can be helpful, but may sometimes lead to unwanted forms, such as factorizations of base numbers.

Domain of the logarithmic function

The command domain(expression, variable) shows the values of the variable for which the expression is defined.

Change of base for logarithms

Use the arrow-templatelogbase() or arrow-templateln command to convert the base of a logarithm. These can be found under 3: Algebra > A. Convert Expression. The arrow arrow-template can be typed as @>.