Question

if 3^x = 5^y = 75^z show that z= xy/2x +y

Answer 1

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^(x-z)/5^2z=5^(y-z)/3^z
3^(x-z)/5^2z=3^-z/5^-(y-2z)
On equating
(x-z) /2z=z/(y-2z)
xy-2xz-yz+2z^2=2z^2
xy-2xz-yz=0
xy-z(2x+y) =0
xy=z(2x+y)
z=xy/(2x+y) hence proved