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Taking Logarithms
CodeExpectedActual
Math.log(1)
 0.0 0.0 
Math.log(Math::E)
 1.0 1.0 
Math.log(10)
 2.30258509299405 2.30258509299405 
Math::E ** Math.log(25)
 25.0 25.0 
Math.log10(1)
 0.0 0.0 
Math.log10(10)
 1.0 1.0 
Math.log10(10.1)
 1.00432137378264 1.00432137378264 
Math.log10(1000)
 3.0 3.0 
10 ** Math.log10(25)
 25.0 25.0 
module Math
  def Math.logb(num, base)
    log(num) / log(base)
  end
end
dividend = Math.log(2)
(1..6).collect { |x| Math.log(x) / dividend }
 [0.0, 1.0, 1.58496250072116, 2.0, 2.32192809488736, 2.58496250072116] [0.0, 1.0, 1.58496250072116, 2.0, 2.32192809488736, 2.58496250072116] 
require 'bigdecimal'
require 'bigdecimal/math'
require 'bigdecimal/util'
module BigMath
  alias :log_slow :log
  def log(x, prec)
    if x <= 0 || prec <= 0
      raise ArgumentError, "Zero or negative argument for log"
    end
    return x if x.infinite? || x.nan?
    sign, fraction, power, exponent = x.split
    fraction = BigDecimal(".#{fraction}")
    power = power.to_s.to_d
    log_slow(fraction, prec) + (log_slow(power, prec) * exponent)
  end
end
include BigMath
number = BigDecimal("1234.5678")
Math.log(number)
 7.11847622829779 7.11847622829779 
prec = 50
BigMath.log_slow(number, prec).round(prec).to_s("F")
 "7.11847622829778629250879253638708184134073214145175" "7.11847622829778629250879253638708184134073214145175" 
BigMath.log(number, prec).round(prec).to_s("F")
 "7.11847622829778629250879253638708184134073214145175" "7.11847622829778629250879253638708184134073214145175" 
BigMath.log(number ** 1000, prec).round(prec).to_s("F")
 "7118.47622829778629250879253638708184134073214145175161" "7118.47622829778629250879253638708184134073214145175161" 
huge_number = BigDecimal("1000") ** 1000
base = BigDecimal("10")
(BigMath.log(huge_number, 100) / BigMath.log(base, 100)).to_f
 3000.0 3000.0