Chapter Exponents and Logarithms
This chapter begins with the algebra of exponents themselves: the rules for combining powers, negative exponents, and the fact that radicals are just fractional powers. Being quick with this algebra—rewriting \(\frac{1}{\sqrt[3]{x^2}}\) as \(x^{-2/3}\) without hesitation—is what makes derivative computations go smoothly later. Exponential functions are functions in which a fixed value is raised to the power of the input variable. Logarithmic functions are the inverses of these. One important related concept is Euler’s number \(e\text{,}\) which has very nice properties as a base and is vital to the exponential and logarithmic functions of calculus.
Topics
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Exponent Rules: Combining powers, negative exponents, simplifying expressions
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Radicals and Rational Exponents: Simplifying radicals, converting between radical and exponent notation
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Exponential Functions: Evaluating exponential expressions/functions and using exponential functions as models
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Logarithm Rules: Rules for adding and scaling logarithms
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Logarithmic Functions: Interpreting and modeling with logarithmic functions
Resources
Chapter 3 of Active Prelude to Calculus.
