Algebra
LOGARITHMS
Examples:
log2 8 = 3
since
8 = 23
log10 0.01 = -2
since
0.01 = 10-2
log5 5 = 1
since
5 = 51
logb 1 = 0
since
1 = b
From the above illustration, it is evident that a logarithm is an exponent. 34 is called the
exponential form of the number 81. In logarithmic form, 34 would be expressed as log3 81 = 4,
or the logarithm of 81 to the base 3 is 4. Note the symbol for taking the logarithm of the
number 81 to a particular base 3, is log3 81, where the base is indicated by a small number
written to the right and slightly below the symbol log.
Log Rules
Since logs are exponents, the rules governing logs are very similar to the laws of exponents.
The most common log rules are the following:
1.
logb (ABC) = logb A + logb B + logb C
2.
logb (A/B) = logb A - logb B
3.
logb (An) = nlogb A
4.
logb b = 1
5.
logb
= logb A1/n = (1/n)logb A
n
A
6.
logb 1 = 0
7.
logb (1/A) = logb 1 - logb A = -logb A
Rev. 0
Page 65
MA-02
