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prove that [(yz)^(logy-logz)][(zx)^(logz-logx)][(xy)^(logx-logy)]=1

prove that [(yz)^(logy-logz)][(zx)^(logz-logx)][(xy)^(logx-logy)]=1

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear Ritish
 
Let : 
K = [(yz)^(log y - log z)] • [(zx)^(log z - log x)] • [(xy)^(log x - log y)] 
Then : 
log K = (log y - log z)· log (yz) + ... two similar terms 
. . . . = (log y - log z)·(log y + log z) + ... two similar terms 
. . . . = [ (log y)² - (log z)² ] + [ (log z)² - (log x)² ] + [ (log x)² - (log y)² ] 
. . . . = 0. 
Since : log K = 0, 
Hence : K = 1. 
Thus, the result is proved. 
 
Regards
Arun (askIITians forum expert)

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