Basic Technical Mathematics, 11th Edition

13.5 Natural Logarithms

• Natural Logarithm (ln x) • Change of Base • Calculator Values and Graphs

As we have noted, another number important as a base of logarithms is the number e. Logarithms to the base e are called natural logarithms. Since e is an irrational number equal to about 2.718, it may appear to be a very unnatural choice as a base of logarithms. However, in calculus, the reason for its choice and the fact that it is a very natural number for a base of logarithms are shown.

Just as $\log x$ refers to logarithms to the base 10, the notation ln x is used to denote logarithms to the base e. We briefly noted this in Section 13.2 in discussing the calculator. Due to the extensive use of natural logarithms, the notation ln x is more convenient ...