* The Law of Logarithms with regard to Powers and Roots of Numbers *

 

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Many times students see no value in these type of problems, however,

when confronted with an  advanced problems  where these laws apply they will.

 

 

The Log of a Power equals the Power X the Log of Number    *   Log (A)P  = P x  Log (A)

 

                          (648)7  =  N                                       Determine the Seventh Power of  (648)

 

            (Log)     (648)7  =  N        (Log)                      Take the Log of both Sides

 

            7 x (Log) (648) = Log N                                 Distribute the Log on both sides

 

                    7 x  _____ = Log N                                Determine Log of ( ) & Multiply by 7

 

               (Anti) _____ = Log  N  (Anti)                     Take the  AntiLog  of both sides

 

                                    _____ = N                               Check N  in   10E = N

 

 

 

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The Log of a Root equals the Root X the Log of Number    *   Log (A)R  = R x  Log (A)

 

                          (.007)1/5 =  N                                     Determine the Fifth Root of  (.007)

 

            (Log)     (648)71/5 =  N      (Log)                      Take the Log of both Sides

 

            (1/5) x (Log) (648) = Log N                           Distribute the Log on both sides

 

               (1/5) x  _____ = Log N                                Determine Log of ( ) & Multiply by (1/5)

 

               (Anti) _____ = Log  N  (Anti)                     Take the  AntiLog  of both sides

 

                                    _____ = N                               Check N  in   10E = N

 

 

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Tom Love                            Malone College                      Fall 2007