Converting Between Logarithmic and Exponential Forms

Miacademy & MiaPrep Learning Channel

This instructional video provides a clear, step-by-step guide on how to convert mathematical expressions between logarithmic and exponential forms. Opening with a brief explanation of why these conversions are useful in science and engineering, the instructor uses a digital whiteboard to demonstrate the structural relationship between the two forms. The video breaks down the specific variables involved—base ($b$), exponent ($x$), and argument ($y$)—and shows how they map onto one another when switching formats. The content covers four distinct examples: two converting from logarithmic to exponential equations, and two converting from exponential to logarithmic equations. The instructor emphasizes a pattern-matching strategy, encouraging viewers to explicitly identify which numbers correspond to the variables $b$, $x$, and $y$ in the standard formulas. This methodical approach helps demystify the often-confusing notation associated with logarithms. Ideally suited for Algebra II and Pre-Calculus classrooms, this video serves as excellent direct instruction or review material. It simplifies abstract notation into a concrete process of rearranging terms. Teachers can use this resource to introduce the definition of a logarithm, reinforce the concept of inverse functions, or support students who struggle with the syntax of logarithmic equations.