The `x , y , z` are positive real numbers such that `(log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3,` then the value of `(1/(2z))` is ............

The x,y,z are positive real numbers such that log_(2x)z=3,log_(5y)z=6, and log_(xy)z=(2)/(3), then the value of ((1)/(2z)) is .........

Let x,y,z be positive real numbers such that log_(2x)z=3, log_(5y)z=6 and log_(xy)z=2/3 then the value of z is

Let x,y,z be positive real numbers such that log_(2x)z=3,log_(5y)z=6 and log_(xy)z=(2)/(3) then the value of z is

Let x,y and z be positive real numbers such that x^(log_(2)7)=8,y^(log_(3)5)=81 and z^(log_(5)216)=(5)^((1)/(3)) The value of (x(log_(2)7)^(2))+(y^(log_(3)5)^^2)+z^((log_(5)16)^(2)), is

If (log a)/(y-z)=(log b)/(z-x)=(log c)/(x-y) the value of a^(y+z)*b^(z+x)*c^(x+y) is

If (log^(2)-2(x+1)+log^(2)-2(log_(3)(y))+log^(2)-2(1+log_(2)(z))=0, then the value of (x+y+z) is -

If x=(log)_(2a)a , y=(log)_(3a)2a ,z=(log)_(4a)3a ,prove that 1+x y z=2y z

If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)