# 4: What about other numbers?

So far we have been finding logs of pretty easy numbers — various arrangements of a ‘1’ and some zeros. So, it’s easy to figure out that log (100) = 2 and log (1000) = 3. But of course (being scientists) we know that the numbers we’re really interested in aren’t going to be so simple.

To what power must 10 be raised in order to obtain the value of 6? The number 6 is between 1 and 10 so the log of 6 must be greater than the log of 1 (i.e. 0) and less than the log of 10 (i.e. 1).  The actual value of log (6) is 0.77815.

How about the log of 180? 279? 736.2? Well, first of all we know that all of the logs for these numbers must be between 2 and 3. But where exactly? There is no easy formula for calculating this … here is a case where you really do need a calculator (or a slide rule, or a lookup table, or enough time to do a little calculus).

The number 6 is between 1 and 10 so the log of 6 must be greater than the log of 1 (i.e. 0) and less than the log of 10 (i.e. 1).  The actual value of log (6) is 0.77815. 