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

Prove that ((log)_(a)N)/((log)_(ab)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 a > 0, c > 0, b = sqrt(ac), ac != 1 and N > 0 , then prove that (log_(a)N)/(log_(c )N) = (log_(a)N - log_(b)N)/(log_(b)N - log_(c )N) .

If agt0,cgt0,b=sqrt(ac),a,c and ac ne 1 , N gt0 prove that (log_(a)N)/(log_(c )N)=(log_(a)N-log_(b)N)/(log_(b)N-log_(c )N)

Prove the identity; (log)_a N* (log)_b N+(log)_b N * (log)_c N+(log)_c N * (log)_a N=((log)_a N*(log)_b N*(log)_c N)/((log)_(a b c)N)

Prove the identity; (log)_a Ndot(log)_b N+(log)_b Ndot(log)_c N+(log)_c Ndot(log)_a N=((log)_a Ndot(log)_b Ndot(log)_c N)/((log)_(a b c)N)

Prove the identity; (log)_(a)N log_(b)N+(log)_(b)N log_(c)N+(log)_(c)N log_(a)N=((log)_(a)N log_(b)N log_(c)N)/((log)_(abc)N)

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .