AlgebraLOGARITHMSBase 10 logs are often referred to as common logs. Since base 10 is the most widely usednumber base, the "10" from the designation log10 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 log10X = 2, then2.0 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 = 3.83860Add the logarithms to get 5.42732Find the anti-log.Anti-log 5.42732 = 2.675 x 105 = 267,500Thus, 38.79 x 6896 = 2.675 x 105 = 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:UsingCommonLogsUsingNaturalLogs2X7log 2Xlog 7X log 2log 7Xlog 7log 20.84510.30102.8082X7ln 2Xln 7X ln 2ln 7Xln 7ln 21.9460.6932.808Rev. 0 Page 69 MA-02
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