AlgebraLOGARITHMSBase 10 logs are often referred to as common logs. Since base 10 is the most widely usednumber base, the "10" from the designation log_{10} is often dropped. Therefore, any time "log" isused without a base specified, one should assume that base 10 is being used.Anti-LogarithmsAn anti-logarithm is the opposite of a logarithm. Thus, finding the anti-logarithm of a numberis the same as finding the value for which the given number is the logarithm. If log_{10}X = 2, then2.0 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 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 = 3.83860Add the logarithms to get 5.42732Find the anti-log.Anti-log 5.42732 = 2.675 x 10^{5} = 267,500Thus, 38.79 x 6896 = 2.675 x 10^{5} = 267,500NaturalandCommonLogOperationsThe 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 equationis as follows:UsingCommonLogsUsingNaturalLogs2^{X}7log 2^{X}log 7X log 2log 7Xlog 7log 20.84510.30102.8082^{X}7ln 2^{X}ln 7X ln 2ln 7Xln 7ln 21.9460.6932.808Rev. 0 Page 69 MA-02

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