6no use of doin such long sums now dude....
If \frac{x(y+z-x)}{log(x)}=\frac{y(z+x-y)}{log(y)}=\frac{z(x+y-z)}{log(z)} ,
prove that:
y^z.z^y=z^x.x^z=x^y.y^x
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2 Answers
11it is quite a long sum...
x(y+z-x)log x = y(z+x-y)log y = z(x+y-z)log z =1k.
thus, log x = k(xy+yz-x2)
log y = k(yz+xy-y2)
log z = k(zx+yz-z2)
R.T.P :- yz.zy = zx.xz
take log,
L.H.S
z log y + y log z
putting the values of log y and log z,
we get, L.H.S. = 2kxyz
R.H.S will give the same thing..
similarly do the other one.. :)
