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We want to compute y = log(x) – log base 10 – using ln() – natural log. y = log(x) is equivalent to:

         y
x  =  10  

Define a = ln(10), then

         a
10  =  e

Substituting

          a   y         (a * y)
x  =  ( e   )    =    e

then

ln(x)  = a * y

Use a = ln(10),

y = ln(x)/ln(10)