A few generations ago, you might have learned how to take logarithms with the slide rule scale. Here I’ll teach you the fast algorithm astronomers use to take logarithms in their head.
Algorithm:
- If the number is already in scientific format (easy case):
- 1 * 10^A, then the log10 is A.
- 3 * 10^A, then the log10 is A.5.
- There are no other numbers, pick the closest of the two cases above.
- If the number is >=1:
- 1xxxxxxxxx: count the number of x digits and call it A –> the log10 is A.
- 3xxxxxxxxx: count the number of x digits and call it A –> the log10 is A.5
- If the number is <1:
- 0.xxxxxx1: the log10 is the number of digits after the period.
- 0.xxxxxx3: the log10 is the number of digits after the period, plus 0.5.
dex: the units of logarithm differences
Finally, we can talk differences in logarithmic plots. A difference of 1 in a log plot is a factor of ten, a difference of 2.5 is a factor of 300.
Astronomers say “dex” after the difference to indicate log-differences. So. “There is a 2.5 dex difference”.
It’s quite nice shorthand.
Astronomers don’t know that non-astronomers (even physicists) don’t know about dex.
dex is analogous to decibel, or magnitudes.
dex stands for decimal exponent.
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