Prove that :

` (1)/( log _(a) ^(abc) )+(1)/(log_(b)^(abc) ) + (1)/( log _c^(abc)) =1`

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

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

Prove that ln(1+x) 0.

1/log_(ab)(abc)+1/log_(bc)(abc)+1/log_(ca)(abc) is equal to:

If (1)/("log"_(2)a) + (1)/("log"_(4)a) + (1)/("log"_(8)a) + (1)/("log"_(16)a) + …. + (1)/("log"_(2^(n))a) = (n(n+1)/(lambda)) then lambda equals

If (1)/(log_(a)x) + (1)/(log_(b)x) = (2)/(log_(c)x) , prove that : c^(2) = ab .

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

Prove that : (i) (log a)^(2) - (log b)^(2) = log((a)/(b)).log(ab) (ii) If a log b + b log a - 1 = 0, then b^(a).a^(b) = 10

(1)/("log"_(2)n) + (1)/("log"_(3)n) + (1)/("log"_(4)n) + … + (1)/("log"_(43)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) .