Posted by tuhituhi on Tuesday, April 9, 2013 at 8:38am.
if 3^x = 5^y = 75^z show that z= xy/2x +y

maths  Simmi Mathuri, Thursday, September 15, 2016 at 12:40am
3^x =5^y=75 ^z
3^x =5^y=(3X5^2) ^z
3^x =5^y=3^zX5^2z
3^x/(3^zX5^2z) =5^z/(3^zX5^2z)
3^(xz)/5^2z=5^(yz)/3^z
3^(xz)/5^2z=3^z/5^(y2z)
On equating
(xz) /2z=z/(y2z)
xy2xzyz+2z^2=2z^2
xy2xzyz=0
xyz(2x+y) =0
xy=z(2x+y)
z=xy/(2x+y) hence proved