Evaluating Logarithms with the Change of Base Formula

The Organic Chemistry Tutor

This educational math tutorial explains how to evaluate logarithms using the Change of Base Formula. The instructor begins by reviewing a simple logarithmic expression that can be solved mentally based on exponential knowledge. He then introduces the Change of Base Formula, explaining its purpose: allowing calculations of logarithms with bases not typically found on standard calculators (like base 2 or base 3) by converting them into a quotient of common logarithms (base 10). The video demonstrates the formula's application using a specific example and verifies the result against the known exponential relationship. The instructor emphasizes that while the formula allows for changing to any base, the practical application usually involves converting to base 10 to utilize standard calculator functions. The lesson concludes with two practice problems involving base 3 and base 7. The instructor walks through the setup for each, calculates the result, and briefly connects the answers back to their exponential forms (e.g., 3 to the 5th power is 243) to reinforce understanding. This resource is highly valuable for algebra students transitioning from conceptual understanding of logs to practical computation.