Natural Logarithms

In most practical applications of logarithms, the irrational number e is used as the base. Logarithms with base e are natural logarithms because they occur in the life sciences and economics in natural

situations that involve growth and decay. The base e logarithm of x is written ln x (read “el-en x”). The expression ln x represents the exponent to which e must be raised in order to obtain x.

What is a Natural Logarithm?

For all positive numbers x,

$\ln x=\log_ex.$

Evaluating Natural Logarithms with a Calculator

Use a calculator to find the values of  $\ln\:e^3,\:\ln142,\:$and $\ln\:0.005832.$

Solution

The exact value of $\ln e^3\:$is 3, and $\ln\:142\approx4.955827058$ and  $\ln0.005832\approx-5.144395284.$