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Anti-Logarithms - h1014v1_183

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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 = 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 Page 69 MA-02



   


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