Question

X^log x^y-log x^x.y^log y z-log y^x^log x^x-log z^y=1​

Answer 1

Answer:

= log[(xy)log(x/y) (yz)log(y/z) (zx)log(z/x)] = log (xy)log(x/y) + log(yz)log(y/z) + log(zx)log(z/x) = log(x/y) log(xy) + log (y/z) log(yz) + log(z/x) log(zx) = (log x – log y) (log x + log y) + (log y – log z) (log y + log z) + (log z – log x) (log z + log x) = (log x)2 – (log y)2 + (log y)2 – (log z)2 + (log z)2 – (log x)2 = 0 => (xy)log(x/y) (yz)log(y/z) (zx)log(z/x) = 1Read more on Sarthaks.com - https://www.sarthaks.com/489750/show-that-xy-log-x-y-yz-log-y-z-zx-log-z-x-1?show=489757#a489757