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.

log_b (x / y) = log_b x – log_b 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.

log_b x – log_b y = log_b (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)