big o - O(log(A)) + O(log(B)) = O(log(A * B))? -

big o - O(log(A)) + O(log(B)) = O(log(A * B))? -

this true:

log(a) + log(b) = log(a * b) [0]

is true?

o(log(a)) + o(log(b)) = o(log(a * b)) [1]

from understand

o(f(n)) + o(g(n)) = max( o(f(n)), o(g(n)) ) [2]

or in other words - if 1 function grows asymptotically faster other function relevant big o notation. maybe equation true instead?

o(log(a)) + o(log(b)) = max( o(log(a), o(log(b)) ) [3]

o linear.

therefore o(a) + o(b) = o(a + b).

so o(log(a)) + o(log(b)) = o(log(a) + log(b)) = o(log(a * b))

concerning [3], right.

if m = o(n) o(n + m) = o(2n) = 2 o(n) = o(n) (2 constant)

big-o complexity-theory