Logarithm of the product (sum of logarithms)

Logarithm of the product is one of the basic logarithmic properties; equals the sum of the logarithms of the factor and the multiplicand, with the base unchanged.

log_b (x ⋅ y) = log_b x+ log_b y

In this case, the result of multiplication x on y must be strictly positive, i.e. (x ⋅ y) > 0.

This property also works in the opposite direction, i.e.:

Sum of logarithms with the same base is equal to the logarithm of the product of their sublogarithmic expressions in the same base.

log_b x+ log_b y = log_b (x ⋅ y)Where x> 0 и y> 0

examples:

• log₃ (5 ⋅ 6) = log₃ 5 + log₃ 6
• log₉ (12 ⋅ 15) = log₉ 12 + log₉ 15
• log₁₁ 7 + log₁₁ 14 = log₁₁ (7 ⋅ 14)