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 log_{10} is often dropped. Therefore, any time "log" is
used without a base specified, one should assume that base 10 is being used.
AntiLogarithms
An antilogarithm is the opposite of a logarithm. Thus, finding the antilogarithm of a number
is the same as finding the value for which the given number is the logarithm. If log_{10} X = 2, then
2.0 is the power (exponent) to which one must raise the base 10 to obtain X, that is, X = 10^{2.0}
= 100. The determination of an antilog 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 antilog.
Antilog 5.42732 = 2.675 x 10^{5} = 267,500
Thus, 38.79 x 6896 = 2.675 x 10^{5} = 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
2^{X}
7
log 2^{X}
log 7
X log 2
log 7
X
log 7
log 2
0.8451
0.3010
2.808
2^{X}
7
ln 2^{X}
ln 7
X ln 2
ln 7
X
ln 7
ln 2
1.946
0.693
2.808
Rev. 0
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MA02

