Pre-Calculus Prep: VOLUME 3: Exponential And Logarithmic Functions

Graphing exponential functions: This topic involves understanding and graphing functions in the form f(x) = a^x, where 'a' is a constant base. It explores the behavior of exponential functions, such as growth or decay rates, asymptotes, and transformations.

Exponential equations not requiring logarithms: This topic focuses on solving equations in the form a^x = b, where 'a' and 'b' are constants. It covers methods like using properties of exponents, simplifying equations, and finding exact or approximate solutions.

Exponents and logarithms: This topic introduces the fundamental concepts of exponents and logarithms. It explores the relationship between these two operations and covers topics such as exponent rules, logarithmic rules, and converting between exponential and logarithmic forms.

Evaluating logarithms: This topic involves computing the values of logarithmic expressions using various bases. It covers techniques for evaluating logarithms using calculators, logarithmic tables, or the change of base formula.

Logarithms and exponents as inverses: This topic explores the inverse relationship between logarithmic and exponential functions. It emphasizes the concept that applying a logarithm undoes the action of an exponential function and vice versa.

Properties of logarithms: This topic covers the properties and rules of logarithms, including the product rule, quotient rule, power rule, and change of base formula. It focuses on using these properties to simplify logarithmic expressions and solve equations.

Writing logs in terms of others: This topic involves expressing logarithms with one base in terms of logarithms with a different base. It explores methods like using the change of base formula or converting between common bases, such as natural logarithms (ln) or base-10 logarithms.

Exponential equations requiring logarithms: This topic deals with solving exponential equations that cannot be simplified or solved using basic algebraic techniques alone. It introduces the use of logarithms to solve equations with exponential terms.

Logarithmic equations, simple: This topic focuses on solving simple equations involving logarithmic expressions. It covers techniques such as isolating the logarithmic term, using logarithmic properties, and finding exact or approximate solutions.

Logarithmic equations, hard: This topic deals with solving more complex logarithmic equations that require algebraic manipulations and multiple steps to solve. It explores advanced techniques such as factoring, combining logarithmic terms, and applying logarithmic identities.

Graphing logarithmic functions: This topic involves understanding and graphing functions in the form f(x) = log(base a) (x), where 'a' is a constant base. It explores the behavior of logarithmic functions, including asymptotes, domain, range, and transformations.

Compound interest: This topic relates to the application of exponential growth in financial contexts. It involves understanding and calculating compound interest using formulas like the continuously compounded interest formula and exploring concepts such as principal, interest rate, and time periods.

These videos are designed to review and reteach Precalculus and Collegeboard Pre-CALC AP content. My videos cover functions, polynomials, exponential and logarithmic expressions, trigonometry, parametric equations, polar coordinates, vectors, matrices and systems, conic sections, discrete mathematics, sequences and series; and an introduction to calculus.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa .
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