working out logs? (algorithms)

Question

can someone please explain to me, how to work out logs?

e.g. log27 to the power 3 ?

I though the above is 3 because 3x3x3=27 and it takes 3, 3's to make 27. is this correct?

Answer 1

The definition of logarithm states that if log_b(x) = y then b^y = x. This works for real numbers, not just integers.

In your example, log₃(27) = 3, because 3³ = 27.

Or your second example: log₃(11) = 2.182658..., because 3^2.182658... = 11.

See Wikipedia.