+Table of Contents
Logarithms
Introduction
The logarithm is the power to which a base must be raised to obtain a particular number. That is:
y=bt iff t=logby |
Manipulating Logarithms
The following rules/results make it relatively easy to manipulate logarithms:
- loguv=logu+logv
- logu/v=logu−logv
- loguk=klogu for u>0
- logbu=(logba)(logau) for u>0
To prove this result let u=ap (so that p=logau). Then:
logbu=logbap=plogba=(logba)(logau) - logbu=1logub
- Combining the previous two rules yields the following “change of base rule”:
logbu=logaulogab for u>0 - ddulogbu=1(ulnb) where ln denotes the natural logarithm (i.e., loge).