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 (a) log ba=log_(a)c(b)log_(c)b=log_(a)c(c)log_(b)a=log_(c)b(d) none of these

a=y^(2),b=z^(2),c=x^(2) then prove that log_(a)x^(3)*log_(b)y^(3)*log_(c)z^(3)=(27)/(8)

if x^(2) + y^(2) = z^(2) then prove that log_(y)(z+x) + log_(y) (z-x)=2

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_(a) x)) and z = a^(1/(1-log_(a)y))",then prove that "x=a^(1/(1-log_(a)z))

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

For positive numbers x ,\ y\ a n d\ z the numerical value of the determinant |1(log)_x y(log)_x z(log)_y x1(log)_y z(log)_z x(log)_z y1| is- a. 0 b. logx y z c. "log"(x+y+z) d. logx\ logy\ logz