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if (log x)/(2a+3b-5c) = (log y)/(2b+3c-5a) = (log z)/(2c+3a-5b) then how is it equal to (log x+log y+log z)/0??And if so then why is (log x+log y+log z)/0 not considered undefined instead(log x+log y+log z)/0 implies log(xyz)=0.why??

if (log x)/(2a+3b-5c) = (log y)/(2b+3c-5a) = (log z)/(2c+3a-5b) then how is it equal to (log x+log y+log z)/0??And if so then why is (log x+log y+log z)/0 not considered undefined instead(log x+log y+log z)/0  implies log(xyz)=0.why??  
 

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1 Answers

Arun
25763 Points
2 years ago
Dear student
 
logx/2a+3b-5c=logy/2b+3c-5a=logx/2c+3a-5bTherefore, we can write it as logx+logy+ logz/0So, logx+ logy+ logz=0So,log(xyz)=0xyz=1

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