Unlock Logarithm Secrets with the Product Rule

Simplify complex logarithmic expressions using the product rule: log(a*b) = log(a) + log(b).

Product Rule of Logarithms

Enter two numbers and a base to calculate the logarithm of their product using the product rule.

Number A

Number B

Base

Result:

Visualization

Logarithm Product Rule Explained

The logarithm product rule is a fundamental property of logarithms that simplifies the logarithm of a product into a sum of logarithms. Specifically, it states that the logarithm of the product of two numbers is equal to the sum of their logarithms. Mathematically, it's expressed as: log_b(mn) = log_b(m) + log_b(n), where 'b' is the base of the logarithm, and 'm' and 'n' are numbers greater than zero. This rule is incredibly useful in simplifying complex logarithmic expressions and is widely applied in various fields like mathematics, physics, and engineering to ease calculations and solve equations. For example, log(10 * 100) = log(10) + log(100) = 1 + 2 = 3.