Solving Exponential Equations: Common Bases, Logarithms, and Quadratics

The Organic Chemistry Tutor

This comprehensive mathematics tutorial provides a step-by-step guide to solving various types of exponential equations. The video progresses from fundamental problems where bases can be matched to more complex scenarios requiring logarithms, natural logarithms, and quadratic factoring. Each example is worked out in real-time on a digital blackboard, demonstrating algebraic manipulation and the properties of exponents. The video explores key themes in Algebra 2 and Pre-Calculus, including the Laws of Exponents, the relationship between exponential and logarithmic functions, and substitution methods for higher-order equations. It specifically covers strategies for handling common bases, using log/ln to solve for exponents, isolating variable terms, and recognizing quadratic structures within exponential forms (hidden quadratics). For educators, this video serves as an excellent instructional resource or review tool for students struggling with the procedural aspects of solving equations. The clear, isolated examples allow for modular teaching—teachers can assign specific segments corresponding to the method currently being taught. It effectively addresses common student hurdles, such as handling fractions as exponents, negative exponents, and factoring out greatest common factors in exponential terms.