Simplify: `1/(1+(log)_a b c)+1/(1+(log)_b c a)+1/(1+(log)_c a b)`

Simplify: (1)/(1+log_(a)bc)+(1)/(1+log_(b)ca)+(1)/(1+log_(c)ab)

If a>1,b>1 and c>1 are in G.P.then show that (1)/(1+(log)_(e)a),(1)/(1+(log)_(e)b), and (1)/(1+(log)_(e)c) are in H.P.

Prove that ((log)_a N)/((log)_(a b)N)=1+(log)_a b

Prove that ((log)_a N)/((log)_(a b)N)=1+(log)_a b

If a ,\ b ,\ c are in G.P. prove that 1/((log)_a m),1/((log)_b m),1/((log)_c m) are in A.P.

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=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 a, b, c are positive real numbers then (1)/("1+log"_(a)bc) + (1)/("1+log"_(b)ca) +(1)/("1+log"_(c)ab)=

1/((log)_(sqrt(b c))a b c)+1/((log)_(sqrt(c a))a b c)+1/((log)_(sqrt(a b))a b c) has the value of equal to: a. 1/2 b. 1 c. 2 d. 4