Definition

The log of N to the base b is the exponent a such that

      N = ba
   

and is written

      logb(N) = a
   

For example,

      1000 = 103,  so log10(1000) = 3

      1024 = 210,  so log2(1024) = 10
   

Logarithms with different Bases

Log to the base 2 is just a constant multiple of the log to the base 10.

Log to base 2 is a (different) constant multiple of the log to any other base b, where the constant depends only on the two bases.

      log2(N) = log10(N) / log10(2)
   

For example, what if N is 2?