Intermediate Algebra | 39.1: The Product Property — Turn a Sum of Logs into One Log

Full course — free exercises, Feynman reviews, and AI-graded feedback: https://ludium.ai/courses/intermediat... A logarithm is just an exponent in disguise, and that single idea makes every logarithm rule easy to remember. In this video we build the product property from the exponent rule you already know, then use it to collapse a sum of same-base logs into one clean logarithm of a product. Key concepts covered: Why a logarithm is really an exponent, and how that mirrors the exponent rules The product property: log of a product equals the sum of the logs Combining two same-base logs that are added into a single logarithm The classic trap: a sum of logs is not the same as the product of two logs Working the property in both directions, but only across multiplication ━━━━━━━━━━━━━━━━━━━━━━━━ SOURCE MATERIALS The source materials for this video are from    • Intermediate Algebra Lecture 12.5:  Explor...