Important Rules for Logarithms

The most important rules for logarithms are

ln (ab) = ln a + ln b,
ln (a^b) = b · ln a.

The natural logarithm function is important in calculus because its derivative is simply 1/x,

, (x > 0).

This can be derived from the Inverse Function Rule.

If 

y = ln x,

then

The natural logarithm is also called the logarithm to the base e and is sometimes written log_e x. Logarithms to other bases are discussed in Chapter 8.