We write the logarithm with base 10 as log(x) and that with base e as ln(x). These are just the inverse functions for the corresponding exponentials, so that
In words, log(x) is the exponent of 10 that gives x, and ln(x) is the exponent of e that gives x, that is,
All logarithm functions have some useful properties:
|logarithm of a product|
|logarithm of a quotient|
|logarithm of a power|
|logarithm of +1|
|logarithm of the base|
|no rules for the logarithm of a sum|
|no rules for the quotient of logarithms|
These follow from the definition of the logarithms as the inverse functions for the corresponding exponential functions.
Be sure you've gone through each step in the examples above before doing these. Once you've worked them until you're sure that you understand them, go on to the next section. There are more problems of this type in the section test at the end of the section.
Note that you can get new practice problems by clicking the "Refresh" button at the bottom of the practice set.