Algebra
LOGARITHMS
Base 10 logs are often referred to as common logs. Since base 10 is the most widely used
number base, the "10" from the designation log10 is often dropped. Therefore, any time "log" is
used without a base specified, one should assume that base 10 is being used.
Anti-Logarithms
An anti-logarithm is the opposite of a logarithm. Thus, finding the anti-logarithm of a number
is the same as finding the value for which the given number is the logarithm. If log10 X = 2, then
2.0 is the power (exponent) to which one must raise the base 10 to obtain X, that is, X = 102.0
= 100. The determination of an anti-log is the reverse process of finding a logarithm.
Example:
Multiply 38.79 and 6896 using logarithms.
Log 38.79 = 1.58872
Log 6896 = 3.83860
Add the logarithms to get 5.42732
Find the anti-log.
Anti-log 5.42732 = 2.675 x 105 = 267,500
Thus, 38.79 x 6896 = 2.675 x 105 = 267,500
Natural and Common Log Operations
The utilization of the log/ln can be seen by trying to solve the following equation algebraically.
This equation cannot be solved by algebraic methods. The mechanism for solving this equation
is as follows:
Using Common Logs
Using Natural Logs
2X
7
log 2X
log 7
X log 2
log 7
X
log 7
log 2
0.8451
0.3010
2.808
2X
7
ln 2X
ln 7
X ln 2
ln 7
X
ln 7
ln 2
1.946
0.693
2.808
Rev. 0
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