MATH REVIEW: USEFUL MATH FOR EVERYONESECTION 4.3. WHAT IS A LOGARITHM? Logarithmic RulesJust as exponents have some basic rules that make them easier to manipulate (see Section 3: Exponents), so do logarithms. These rules apply to all logarithms, including base 10 logarithms and natural logarithms. For simplicity's sake, base ten logs are used in most of these rules:
Let's take a closer look at each of these rules:
1. b^{r} = a is the equivalent of log_{b} a=r. We've already looked at how this works, but here's another example:
is the equivalent of
2. log 0 is undefined. It's not a real number, because you can never get zero by raising anything to the power of anything else. You can never reach zero, you can only approach it using an infinitely large and negative power.
3. log 1 = 0 means that the logarithm of 1 is always zero, no matter what the base of the logarithm is. This is because any number raised to 0 equals 1. Therefore, ln 1 = 0 also. All the rest of the logarithmic rules are useful for solving complex equations, or equations with unknowns. For more information about this site contact the Distance Education Coordinator. Copyright © 2004 by the Regents of the University of Minnesota, an equal opportunity employer and educator. |