Logarithm of division (quotient) or difference of logarithms

Division/quotient (or fraction) logarithm equals the difference between the logarithms of the dividend and the divisor (numerator and denominator) with the same base.

logb (x / y) = logb x – logb y

Required condition: (x/y) > 0.

This is one of the main properties of logarithms, which can be represented in reverse order:

Difference of logarithms with the same bases is equal to the logarithm of the quotient / division or a fraction consisting of sublogarithmic expressions. The base does not change.

logb x – logb y = logb (x / y)At x> 0 и y> 0

examples:

  • log6 (5 / 8) = log6 5 – log6 8
  • log16 (15 / 5) = log16 15 – log16 5
  • log5 9 – log5 4 = log5 (9 / 4)

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