Properties of Logarithmic Functions and Expressions Video 1

Explaining the basic properties of logarithmic functions

Explaining how to solve logarithmic equations

Explaining how to solve equations with power and exponential terms

Finding the domain of a function with a root and a logarithm in the denominator

Solving logarithmic equations with a single logarithm term

Solving logarithmic equations with multiple logarithm terms

Solving logarithmic equations with multiple logarithm terms on both sides

Solving equations with exponential terms

Solving equations with base e exponential terms

Explaining the formulas for the derivatives of exponential functions

Solving a equation with an exponential function

Solving an equation with two exponential functions with different bases

Proving facts about logarithms and exponentials including the derivative of an exponential with an arbitrary base

Solving an equation with exponential functions by factoring

Solving a equation with exponential functions by factoring

Solving an equation an exponential function

Solving an equation with exponential functions

Solving an equation with a logarithmic function

Solving an equation with several logarithmic functions

Evaluating a logarithm inside an exponential function

Writing logarithmic equations in exponential form

Solving equations with exponentials and logarithms

Solving equations with exponentials and logarithms

Solving equations with exponentials and logarithms

Using logarithmic differentiation to find the derivative of a function

Using logarithmic differentiation to find the derivative of a function

Using logarithmic differentiation to find the derivative of a function

Evaluating a limit with an indeterminate power using L'Hospital's Rule

Evaluating a limit with an indeterminant power using L'Hospital's Rule

Expanding logarithmic expressions using logarithm rules

Condensing a logarithmic expression into a single logarithm

Using logarithms to transform an exponential function to a linear function

Using the formula to change the base of a logarithm

Using the formula to change the base of a logarithm

Solving an equation with logarithmic functions

Solving an equation with logarithmic functions

Solving an equation with logarithmic functions

Solving an equation with logarithmic functions

Solving an equation with logarithmic functions

Explaining domain restrictions for denominators, even roots, and logarithms

Properties of exponential growth and decay functions

Properties of the exponential function with base e

Properties of exponents applied to power and exponential expressions

Properties of multiplying and simplifying power and exponential expressions

Properties of exponents applied to power and exponential expressions

How to rewrite radical terms as power terms

Explaining the main three forms for linear equations

Discussing properties of linear functions

Discussing the types of linear graphs including horizontal and vertical lines and their properties

Explaining the general properties of even and odd root functions

Discussing parent functions of rational functions and their properties

Finding horizontal asymptotes for rational functions

Explaining the standard form for a quadratic equation and the possible number of solutions

Explaining the graph and properties for the parent function of quadratics

Discussing properties of quadratic functions including the vertex, domain, range, and end behavior

Explaining basic algebraic operations for fractions

Explaining the format and possible solutions for a system of two linear equations

Finding the composition of two functions with exponentials and logarithms

Condensing logarithmic expressions into a single logarithm

Explaining the logarithmic scale and a semilog plot

Calculating a derivative of a quotient with an exponential function

Derivatives of exponential and logarithmic functions and the exponential model

Derivatives of exponential and logarithmic functions and the exponential model

Finding the domain and x-intercepts of a logarithmic function

Finding the domain and x-intercepts of a logarithmic function

Finding the domain of a function with a denominator, square root, and logarithm

Finding the domain of a function with a natural logarithm and denominator

Finding the domain of a logarithmic function

Using logarithms to transform a power function into a linear function

Finding the exact value of logarithms using logarithmic properties

Expanding a logarithmic expression using logarithm properties

Finding the derivative a function with a power, exponential, and logarithm

Solving an indefinite integral by first simplifying the fraction

Examples of integration by substitution

Using L'Hospital's Rule to solve limits

Using properties of logarithms to determine whether a statement is true or false

Finding the domain of a function containing a logarithm, exponential, and fraction

Using properties of logarithms to determine whether a statement is true or false

Expressing a combination of logarithms as a single logarithm

Finding the domain, range, end behavior, and intercepts for a logarithmic function

Finding the domain of a function containing a logarithm, exponential, radical, and fraction

Using properties of logarithms to write an expression as a single logarithm

Solving an improper integral where the upper limit of integration is infinity

Finding the limit of a sequence using logarithm properties

Using logarithmic differentiation to find the derivative of a function

Evaluating a definite integral with an exponential and sine function

Evaluating a limit at infinity by combining logarithms

Finding a derivative using the Chain Rule and Product Rule

Using the Product and Chain Rules to differentiate functions with logarithms

Differentiating functions with logarithmic and inverse trigonometric functions

Using logarithmic differentiation to find the derivative of a function

Using logarithmic differentiation to find the derivative of a function

Evaluating a limit using L'Hospital's Rule

Antidifferentiating twice to find a function from its second derivative

Antidifferentiating to find a function from its derivative

Antidifferentiating twice to find a function from its second derivative

Antidifferentiating twice to find a function from its second derivative

Using antidifferentiation to find the height of a cliff from the impact speed of a dropped stone

Evaluating a limit using logarithm properties

Evaluating a limit using L'Hospital's Rule

Evaluating a limit with an indeterminant power using L'Hospital's Rule

Performing basic numerical calculations in Python

Using the second derivative to find the maximum rate of change in a word problem

Simplifying power and exponential expressions using properties of exponents

Simplifying power and exponential expressions using properties of exponents

Simplifying an expression with both power and exponential functions using properties of exponents

Mean Value Theorem and using derivatives to find the shape of curves

Derivatives of exponential functions and the exponential model

Using Reimann sums and the Fundamental Theorem of Calculus

Using Riemann sums and the Fundamental Theorem of Calculus

Writing a non-linear function to represent the line graphed on a semilog plot

Solving a logarithmic equation using properties of logarithms

Solving a logarithmic equation using properties of logarithms

Using logarithm properties to simplify before using the Chain Rule to find a derivative

Using logarithm properties to simplify before using the Generalized Logarithm Rule to find a derivative

Finding the derivative of a function that requires logarithmic differentiation

Using the alternate form of the Chain Rule to find the derivative

Using the Generalized Exponential Rule to find the derivative of a function

Finding the vertical asymptote of a logarithmic function

Finding the vertical asymptote of a logarithmic function

Determining if a sequence is increasing, decreasing, or not monotonic and if it is bounded

Finding a power series representation for a function

Determining the graph of a logarithmic function

Using the properties of logarithms to expand a logarithmic expression

Using the properties of logarithms to expand a logarithmic expression

Using the properties of logarithms to condense the expression as a single logarithm

Using the properties of logarithms to condense the expression as a single logarithm

Solving an equation with an exponential function

Solving an equation with an exponential function

Solving an equation with an exponential function

Solving an equation with exponential functions by factoring

Modeling a population size with an exponential function

Simplifying logarithmic expressions using the properties of logarithms

Determining the properties of a logarithmic function

Determining the graph of a logarithmic function

Determining the properties of a logarithmic function

Using Python to approximate a definite integral using left endpoint Riemann sums

Approximation and Newton's Method, and limits and derivatives of exponential functions

Approximation and Newton's Method, and limits and derivatives of exponential functions

Determining where a function with a fraction, square root, and logarithm is continuous

Explaining the definition of logarithmic scale and double-log plots

Calculating the derivative of a function with exponentials using the chain and product rule

Proving the derivative of ln(x) and the power and product rules using logarithmic differentiation

Finding the domain of a function with a square root in the denominator

Finding the domain of even and odd roots

Finding the domain of functions with even and odd roots

Finding the domain of several rational functions

Finding the domain of a rational function

Explaining how to find any holes and vertical asymptotes of a rational function

Finding the domain of a rational function using factoring

Writing a non-linear function for the graph containing two points on a double-log plot

Explaining exponential functions in discrete time

Solving a population example of exponential growth in discrete time

Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine

Finding the antiderivative of a function

Evaluating an indefinite integral with an exponential

Using u-substitution in an indefinite integral to find a function from its derivative and a given vaue

Finding the nth Taylor polynomial of the natural log function centered at 1

Finding the horizontal asymptotes of a function that is a fraction with exponentials in the numerator and denominator

Finding the horizontal asymptote of an exponential function

Finding the horizontal asymptote of an exponential function

Finding the horizontal asymptote of an exponential function

Using u substitution to evaluate integrals and prove facts about logarithms and integrals and

Finding a partial fraction decomposition and integrating using partial fractions

Proving L'Hospital's Rule and using it to evaluate limits

Solving the limits approaching infinity and negative infinity with exponential functions in the numerator and denominator

Discussing how to write the equation of a line through two given points

Writing a linear equation of profit from a business word problem

Rewriting a function with a fractional exponent in radical form

Finding the properties of an exponential function including domain, range, end behavior, and intercepts

Finding the properties of an exponential function including domain, range, end behavior, and intercepts

Finding the properties of an exponential function including domain, range, end behavior, and intercepts

Finding the domain of a function that is a fraction containing an exponential and root

Finding the domain of a function that is a fraction containing an exponential and root

Finding the domain of a function that is a fraction containing exponentials and a square root

Solving an equation with exponential functions

Solving an equation with exponential functions

Calculating how much to invest with continuously compounded interest

Identifying the parent function and transformations for a given graph

Identifying the parent function and transformations in order for a given function

Finding the domain of a function containing several logarithms

Stating the domain in interval notation of a function with radicals, fractions, and exponentials

Calculating continuously compounded interest for money in an account

Find the domain of a function in interval notation with a fraction and logarithm

Solving an improper integral where the upper limit of integration is infinity

Solving an improper integral where the upper limit of integration is infinity

Solving an indefinite integral with an exponential function using integration by parts

Solving a definite integral with an exponential function using integration by parts

Solving an indefinite integral with a natural logarithm using integration by parts

Solving a definite integral with a natural logarithm using integration by parts

Solving an indefinite integral with an exponential function using integration by parts

Using integration by parts twice for an integral with sine and an exponential function

Finding the limit of a sequence

Finding the sum of a telescoping series using logarithm properties

Using u-substitution to evaluate a definite integral with a natural logarithm

Using u-substitution on an indefinite integral with an exponential function, sine, and cosine

Using u-substitution to solve an indefinite integral with an exponential function

Mean Value Theorem and properties of a graph

Mean Value Theorem and properties of a graph

Using L'Hospital's Rule to solve a limit with an indeterminant product