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 (log)_b a=(log)_a c b. (log)_c b=(log)_a c c. (log)_b a=(log)_c b d. none of these

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

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 a, b, c are in geometric progression, and if a^(1/x)=b^(1/y)=c^(1/z) , then prove that x, y, z are in arithmetic progression.

If a,b,c are in geometric progression, and if a^(1/x) = b^(1/y) =c^(1/z) , then prove that x,y,z arithmetic progression.

If y= 2^((1)/(log_(x)4)) then prove that x=y^(2) .

f x^(2) + y^(2)= 25xy , then prove that 2 log(x + y) = 3log3 + logx + logy.

If a,b,c are in geometric progression and if a^((1)/(x))=b^((1)/(y))=c^((1)/(z)) , then prove that x,y,z are in arithmetic progression.

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

If in A B C , the distances of the vertices from the orthocentre are x, y, and z, then prove that a/x+b/y+c/z=(a b c)/(x y z)