log question

By using the change-of-base method......for example....suppose we have

log₃ 7     ........the answer to this is given by:     log(7) / log(3)  ≈ 1.77

So......as long as a, b > 0    and a not equal to 1, we have

log_a b =     log(b) / log(a)

Example: What is log of 15 to base 3:

First you take log(15) to base 10=1.176

Next you take log(3) to base 10  =.477

Then you just divide log(15) by log(3), thus:

1.176/.477=2.4654, which is log(15) to base 3, because,

3^2.4654=15-very nearly, because of rounding off.