Solving Logarithmic and Exponential Problems Step-by-Step

The Organic Chemistry Tutor

This comprehensive mathematics tutorial guides students through ten distinct practice problems focused on logarithmic and exponential functions. The video serves as an intensive review session, moving systematically from basic properties to complex equation solving and real-world applications. The narrator uses a digital whiteboard to demonstrate step-by-step solutions, employing color-coded writing to distinguish between steps, properties, and final answers, making the algebraic manipulations easier to follow. Key mathematical themes include the laws of logarithms (product, quotient, and power rules), expanding and condensing logarithmic expressions, and finding the domain and range of functions. The video also covers solving logarithmic and exponential equations by finding common bases or converting forms. Finally, it applies these concepts to word problems involving compound interest and radioactive decay half-life, demonstrating two different methods for solving decay problems: conceptual reasoning and the continuous decay formula. This resource is highly valuable for Algebra II and Pre-Calculus classrooms as a review tool or a flipped classroom resource. It reinforces procedural fluency with logarithms, a topic that often confuses students due to its abstract notation. Teachers can use specific segments to model problem-solving strategies, particularly for identifying extraneous solutions, determining domain restrictions, and setting up exponential growth/decay models.