Why there's no need to specify a base ?

[hentaiw]

Show that for any two bases a and b for logarithms, if a and b are both greater than 1, then
there is a constant c such that loga N ≤ c(logb N). Thus, there is no need to specify a base in
O(log N). That is, O(loga N) and O(logb N) mean the same thing.

I solved this problem,but I didn't understand this sentence .

Thus, there is no need to specify a base in
O(log N).

Why ?

Thanks in advance.

[Gaminic]

if you "solved this problem", you should understand that sentence. You can't have one without the other.

[eypros]

I don't think that the problem you specify has nothing to do with c++. Base in your case mean base of your logarithm:
ln has base e
log has base 10 etc

[hentaiw]

This is just math sorry ,plz move to appropriate forum if you want.

but
loga N < logb N so the 2 log are different not the same,how can we ignore the base.?

[ne555]

Because you don't care about multiplicative constants.
You could be more strict and say log_a N = \alpha log_b N