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

  • maths -

    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

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