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Vignesh A.S. Grade: 8
        


Given Logzxy= c-1, logxyz = a-1, logyzx = b-1, show that ab + bc + ca = abc.


7 years ago

Answers : (2)

Viranch Mistry
32 Points
										

logzxy= c-1   =>  logzxy +1= c  =>  logzxy + logzz = c   =>  logzxyz = c


Thus we have, c = logzxyz,  a= logxxyz  and   b= logyxyz


Now, LHS =   ab + bc +ca  


let us first consider 'ab' ..... ab =  (logxxyz).(logyxyz)  =  [(logexyz)/(logex)] . [(logexyz)/(logey)]


                                                                            =  (logexyz)2 / logx.logy


Simlarly find bc and ac and add you will get     (logexyz)3 / logx.logy.logz


And RHS = abc = (logexyz)3 / logx.logy.logz


Therefore, LHS = RHS !! :)

7 years ago
Anish Nair
19 Points
										

c-1=Logzxy


c=Logzxy +1


c= Logzxy+Logzz


c= Logz(xyz) --1


Similarly,


b= Logyxyz


a= Logxxyz 


put the values of a b c in given equation and get the result

7 years ago
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