If `a^x=b^y=c^z` and `b^2=a c ,` then show that `y=(2z x)/(z+x)`

If a^x=b^y=c^z\ a n d\ b^2=a c , prove that y=(2x z)/(x+z)

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.

If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

If a = b^(2x) , b = c^(2y) and c = a^(2z) , show that 8xyz = 1.

If x/a=y/b=z/c, then show that (x^3+a^3)/(x^2+a^2)+(y^3+b^3)/(y^2+b^2)+(z^3+c^3)/(z^2+c^2)=((x+y+z)^3+(a+b+c)^2)/((x+y+z)^2+(a+b+c)^2).

If y^2=x z and a^x=b^y=c^z , then prove that (log)_ab=(log)_bc

If x,y,z are in G.P and a^x=b^y=c^z ,then

If x = a sec A cos B, y = b sec A sin B and z = c tan A, show that : (x^(2))/ (a^(2)) + (y^(2))/ (b^(2)) - (z^(2))/(c^(2)) = 1

If x=asecthetacosvarphi,\ \ y=bsecthetasinvarphi and z=ctantheta , show that (x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(c^2)=1