In this way, logarithms enable us to write any positive number as a power of ten. Doing that makes many calculations easier and also reveals surprising connections between numbers. Look what happens if we multiply 90 by a factor of 10 or 100 and then take its log again: log 900 ≈ 2.9542 . . . and log 9000 = 3.9542 . . . . Observe two striking things here: All the logs here have the same decimal part, .9542 . . . . Multiplying the original number, 90, by 10 increased its log by 1. Multiplying it by 100 increased its log by 2, etc. We can explain both of these facts by appealing to a
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