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86 THE FASCINATION OF NUMBERS

Therefore, in order to obtain the logarithm to base 10 of any
number, we divide the logarithm to base 2, by the constant
3-322. This can be proved as follows. Let N be any number,
so that N'=10"

Then: n=Log, 0 N' . } . 20 0)
But N=10" and 10=23%322
Therefore Jnzgtaite
and 3-322n=Log, N
But n=Log;, N (from (i) above)
SO 3:322 Log;, N=Log, N

Log, ;
and Logm N=3—§—222—
In general the relationship becomes:
Log, N
LOga N—m

where b is the original base number and & is the base to
which the original logarithm is to be converted.