Logarithm tricks

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properties of logs

Change of log base

If you want to work with an arbitrary base, but you have a log function of which you cannot change the base (e.g. on a calculator), then a useful property is:

logw v = ( logh v ) / ( logh w )


w is the base you want
h is the base you have (which you don't even have to know the value of, just has to be consistent just has to be consistent between the two uses)
v is the value you want the logw of

Say you want the log-base-2 of 256

...but are working with base 10
log2(256) = ( log10(256) ) / ( log10(2) ) ≈ 2.40824 / 0.30103 ≈ 8
...or are working with base e
log2(256) = ( loge(256) ) / ( loge(2) ) ≈ 5.54518  / 0.69315 ≈ 8

addition is multiplication

logb(x*y) = logb x + logb y

subtraction is division

logb(x/y) = logb x - logb y



Decibels are logarithms applied to ratios of power.

Which turns out to be rather useful idea.

Log probabilities