How to Condense Logarithmic Expressions

The Organic Chemistry Tutor

This mathematics tutorial provides a step-by-step guide on how to condense multiple logarithmic expressions into a single logarithm using the properties of logarithms. The video functions as the inverse to a previous lesson on expanding logarithms, focusing now on combining terms. It progresses from simple variable expressions to more complex problems involving integer coefficients and finally rational (fractional) coefficients. The content covers three main properties of logarithms: the Product Rule (addition becomes multiplication), the Quotient Rule (subtraction becomes division), and the Power Rule (coefficients become exponents). The instructor demonstrates these rules through three distinct examples, clearly showing how to handle positive and negative terms to determine their placement in the numerator or denominator of the final argument. This video is highly valuable for high school Algebra II and Pre-Calculus classrooms. It offers clear, procedural modeling for a skill that often confuses students—specifically the order of operations when condensing logs (dealing with coefficients first) and converting fractional exponents into radical form. It serves as an excellent resource for direct instruction, review, or remediation for students struggling with logarithmic properties.