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# Exponential & logarithmic functions

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Multiplying & dividing powers (integer exponents)Powers of products & quotients (integer exponents)

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Intro to square rootsUnderstanding square rootsIntro to cube rootsSquare root of decimal5th roots

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Intro to rational exponentsRewriting roots as rational exponentsExponential equation with rational answer

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Rewriting quotient of powers (rational exponents)Rewriting mixed radical and exponential expressions

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Evaluating fractional exponentsEvaluating fractional exponents: negative unit-fractionEvaluating fractional exponents: fractional baseEvaluating quotient of fractional exponentsEvaluating mixed radicals and exponents

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Simplifying square rootsSimplifying square roots (variables)Simplifying square-root expressionsSimplifying square roots review

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Simplifying higher-index rootsSimplifying cube root expressionsSimplifying cube root expressions (two variables)Simplifying higher-index root expressions

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Simplifying square-root expressions: no variablesSimplifying square roots of fractionsSimplifying rational exponent expressions: mixed exponents and radicalsSimplifying square-root expressions: no variables (advanced)Intro to rationalizing the denominatorWorked example: rationalizing the denominatorSimplifying radical expressions (addition)Simplifying radical expressions (subtraction)Simplifying radical expressions: two variablesSimplifying radical expressions: three variablesSimplifying hairy expression with fractional exponents

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Intro to exponential functionsExponential vs. linear growthExponential vs. linear models: verbalExponential vs. linear models: table

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Exponential expressions word problems (numerical)Initial value & common ratio of exponential functionsExponential expressions word problems (algebraic)Interpreting exponential expression word problem

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Exponential function graphGraphs of exponential growth

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Exponential vs. linear growth over time

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Exponential decay introGraphing exponential growth & decayExponential growth & decay word problems

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Writing exponential functionsWriting exponential functions from tablesWriting exponential functions from graphsAnalyzing tables of exponential functionsAnalyzing graphs of exponential functionsAnalyzing graphs of exponential functions: negative initial valueModeling with basic exponential functions word problem

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Rewriting exponential expressions as A⋅BᵗEquivalent forms of exponential expressions

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Solving exponential equations using exponent propertiesSolving exponential equations using exponent properties (advanced)

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Exponential growth & decay word problems

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Interpreting change in exponential modelsInterpreting time in exponential models

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Constructing exponential modelsConstructing exponential models: half lifeConstructing exponential models: percent changeConstructing exponential models (old example)

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Interpreting change in exponential models: with manipulationInterpreting change in exponential models: changing unitsStructure in exponential expression

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Linear vs. exponential growth: from dataLinear vs. exponential growth: from data (example 2)Comparing growth of exponential & quadratic models

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Intro to logarithmsIntro to LogarithmsEvaluating logarithms (advanced)Relationship between exponentials & logarithmsRelationship between exponentials & logarithms: graphsRelationship between exponentials & logarithms: tables

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𝑒 and compound interest𝑒 as a limitEvaluating natural logarithm with calculator

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Intro to logarithm properties (1 of 2)Intro to logarithm properties (2 of 2)Intro to logarithm propertiesUsing the logarithmic product ruleUsing the logarithmic power ruleUsing the properties of logarithms: multiple stepsProof of the logarithm product ruleProof of the logarithm quotient and power rulesJustifying the logarithm properties

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Evaluating logarithms: change of base ruleLogarithm change of base rule introUsing the logarithm change of base ruleProof of the logarithm change of base ruleLogarithm properties review

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Logarithmic equations: variable in the argumentLogarithmic equations: variable in the base

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Solving exponential equations using logarithms: base-10Solving exponential equations using logarithmsSolving exponential equations using logarithms: base-2

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Exponential model word problem: medication dissolveExponential model word problem: bacteria growth

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Transforming exponential graphsTransforming exponential graphs (example 2)Graphing exponential functionsExponential function graphGraphs of exponential functions (old example)

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Graphical relationship between 2ˣ and log₂(x)Shape of a logarithmic parent graphGraphs of logarithmic functionsVertical asymptote of natural log

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Logarithmic scale (with Vi Hart)Logarithmic scaleRichter scaleBenford's law (with Vi Hart, 1 of 2)Benford's law (with Vi Hart, 2 of 2)

Test your understanding of

**Exponential & logarithmic functions**with these 42 questions.