Exponential and logarithmic functions
Find here some great lessons about exponential and logarithmic functions. Study the lessons below in the order given from top to bottom.
What are exponential functions?
This section will define, write, evaluate, and graph exponential functions. We will also model exponential growth and decay.
Bonus lesson: The exponential growth of coronavirus
What is an exponential function?
Definition of exponential function and some examples of functions that are exponential functions.
Evaluate an exponential function
Learn to evaluate an exponential function to solve real-world problems.
Write an exponential function
learn how to write an exponential function from two points on the function's graph.
What is an exponential growth?
Learn to recognize real-life examples of exponential growth.
Graphing exponential growth
Graphing exponential growth using a table of values.
Modeling exponential growth
Modeling exponential growth with the exponential function y = abx
The exponential growth of coronavirus
Learn how the model the number of deaths that coronavirus may cause
What is exponential decay?
Learn to recognize real-life examples of exponential decay.
Graphing exponential decay
Graphing exponential decay using a table of values.
Modeling exponential decay
Modeling exponential decay with the exponential function y = abx
What are logarithmic functions?
This section will define, evaluate, simplify, expand, and solve logarithmic functions. Three important properties of logarithms are also given.
Interesting topic: The logarithm of a negative number
What is a logarithm?
Learn what a logarithm is and its relationship with the exponential function.
What is the logarithm of a negative number?
A crystal clear explanation showing why the logarithm of a negative number or the logarithm of 0 is undefined.
How to evaluate logarithms
Learn how to evaluate logarithms to find the exponent
Properties of logarithms
Power property, product property, and quotient property
How to simplify logarithms
Simplify a logarithmic expression by writing it as a single logarithm
Expanding logarithms
Express a single logarithm into many individual logarithms.
How to solve exponential equations
Solve exponential equations by taking the log of each side of the equation.
How to solve logarithmic equations
Learn how to solve two types of logarithmic equations.
Graph of exponential and logarithmic function.
The graph of an exponential function is shown in green. The graph shown in light red is the inverse of the exponential function. The line y = x is actually the line of symmetry between the exponential function and the logarithmic function.