Vijay Luxmi Askiitiansexpert
Last Activity: 16 Years ago
Logs to the base 10 are often call common logs, whereas logs to the base e are often call natural logs. Logs to the bases of 10 and e are now both fairly standard on most calculators. Often when taking a log, the base is arbitrary and does not need to be specified. However, at other times it is necessary and must be assumed or specified.
The Four Basic Properties of Logs
- logb(xy) = logbx + logby.
- logb(x/y) = logbx - logby.
- logb(xn) = n logbx.
- logbx = logax / logab.
These four basic properties all follow directly from the fact that logs are exponents. In words, the first three can be remembered as: The log of a product is equal to the sum of the logs of the factors. The log of a quotient is equal to the difference between the logs of the numerator and demoninator. The log of a power is equal to the power times the log of the base.
Additional properties, some obvious, some not so obvious are listed below for reference. Number 6 is called the reciprocal property.
- logb1 = 0.
- logbb = 1.
- logbb2 = 2.
- logbbx = x.
- blogbx = x.
- logab = 1/logba.