If `y=a^(1/(1-(log)_a x))` and `z=a^(1/(1-(log)_a y))`,then prove that `x=a^(1/(1-(log)_a z))`

If y=a^(1/(1-log_ax)), z=a^(1/(1-log_ay)) then prove that x=a^(1/(1-log_az))

If y = a^(1/(1-log_(a)x)) and z = a^(1/(1-log_(a)y)) , then show that x = a^(1/(1-log_(a)z))

If y=a^(1/(1-log_a x)), z=a^(1/(1-log_a y)), then the value of a^(1/(1-log_a z)) is (i) x/y (ii)y/x (iii)z/y (iv) x

If (log x)/(y-z) = (log y)/(z-x) = (log z)/(x-y) , then prove that xyz = 1 .

If (log x)/(y-z)=(log y)/(z-x)=(log z)/(x-y), then prove that: x^(x)y^(y)z^(z)=1

If (log x)/(y-z)=(logy)/(z-x) =(logz)/(x-y) , then prove that: x^x y^y z^z=1

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

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 y=(log)_a x , find (dy)/(dx) .

If ("log"x)/(y - z) = ("log" y)/(z - x) = ("log" z)/(x - y) , then prove that xyz = 1.