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

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

If x^(a) = y^(b) = z^ (c ) and y^(2) = xz, prove that b= ( 2ac)/( a+c)

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

If x=1+(log)_a b c ,\ y=1+(log)_b c a\ a n d\ z=1+(log)_c a b ,\ then prove that x y z=x y+y z+z xdot

If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n d z=c+c/(r^2)+c/(r^4)+oo, prove that (x y)/z=(a b)/c

If tan x =(2b)/ (a- c) , y = acos^2 x + 2bsin x cos x + csin^2 x , z=asin^2 x-2b sin x cos x + c cos^2 x , prove that y-z=a-c .

If a x_1^2+b y_1^2+c z_1^2=a x_2 ^2+b y_2 ^2+c z_2 ^2=a x_3 ^2+b y_3 ^2+c z_3 ^2=d ,a x_2 x_3+b y_2y_3+c z_2z_3=a x_3x_1+b y_3y_1+c z_3z_1=a x_1x_2+b y_1y_2+c z_1z_2=f, then prove that |(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3,y_3,z_3)|=(d-f){((d+2f))/(a b c)}^(1//2)

If a,b,c,d are in GP and a^x=b^y=c^z=d^u , then x ,y,z,u are in