prove that [(yz)^(logy-logz)][(zx)^(logz-logx)][(xy)^(logx-logy)]=1
ritish , 7 Years ago
Grade 11
Magical Mathematics[Interesting Approach]> prove that [(yz)^(logy-logz)][(zx)^(logz-...
1 Answers
Arun
Last Activity: 7 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.
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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