Proving Logarithmic Equations Using the Change of Base Formula

The Organic Chemistry Tutor

This educational video provides a detailed mathematical tutorial on proving logarithmic equations using the Change of Base formula. The instructor guides viewers through three distinct examples of increasing complexity, demonstrating how to manipulate logarithmic expressions to prove that the left side of an equation is identical to the right side. The video focuses specifically on handling logarithms with bases that include radicals or exponents, showing how to convert them into standard forms to verify mathematical truths. Key mathematical themes include the Change of Base formula, the properties of exponents (specifically converting radicals to fractional exponents), and the rules for manipulating logarithmic arguments and coefficients. The video systematically breaks down the process of converting a logarithm with a complex base (like the square root of 'a') into a fraction of two simpler logarithms, simplifying that fraction, and then recombining terms to complete the proof. It also covers handling negative exponents and reciprocals within logarithmic structures. For educators, this video serves as an excellent resource for Algebra II, Pre-Calculus, or College Algebra classrooms. It models clear, step-by-step procedural thinking and reinforces the connection between exponent rules and logarithmic properties. Teachers can use this video to scaffold instruction on mathematical proofs, helping students move beyond simple computation to understanding the structural relationships between different logarithmic forms. The clear handwriting and verbal explanations make it ideal for flipped classroom assignments or review sessions.