SOLUTION: log base x (w)=24, log base y (w)=40, log base xyz (w)=12. Find log base z (w).

You are given

 = 24,      (1)

 = 40,      (2)

 = 12.    (3)



(1) is equivalent to    = w,          (1')

(2) is equivalent to    = w,          (2')

(3) is equivalent to    = w.       (3')


From (3')    = ,   or    = .    (4)


Replace here   by   based on (1').   Replace    by ,  based on (2').  Then you will get


 = ,    which implies

 =   and then   = w.


The last equality means that   = 60.


Answewr.   = 60.

log base x (w)=24, log base y (w)=40, log base xyz (w)=12. Find log base z (w).

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                          . Substituting  for x, and  for y, we get:
      
            ----- Dividing each side by 
           
                
            
               
                 
          --- Raising each side to the 5th power 
                        
              ------- Converting to LOGARITHMIC form