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Log a/y-z=log b/z-x= log c/x-y=k
x Log a=k(y-z)
y log b=k(z-x)
Z log c=k(x-y)
Add all the above equations
log a^x+log b^y+log c^z=k[y-z+z-x+x-y]
Log[a^x b^y c^z] =0=log 1
a^x b^y c^z=1
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