This course is designed for college/university students who want to learn logarithms or just need a refresher. No previous knowledge of logarithms is assumed, so this course is also great for high school students who are just starting the topic. Logarithms are a key concept for any precalculus or calculus student to master.
By taking this course, you will be able to calculate any logarithm with ease, use logarithm rules like a wizz and solve exponential and logarithmic equations in your sleep!
Learn the definition of a logarithm and how to convert between logarithmic form and exponential form.
Learn how to evaluate a logarithm by converting the question to an exponent question.
Learn four important properties of logarithms and why they are true.
Practice examples using the definition of a logarithm and their important properties.
Test your understanding of the definition of a logarithm and the properties of logarithms.
Understand and prove the rule for the log of a product. Learn how it is put to use in practice.
Understand and prove the rule for the log of a quotient. Learn how it is put to use in practice.
Understand and prove the rule for the log of a power. Learn how it is put to use in practice.
Put the three log rules to practice and understand how to avoid the common misconceptions of these rules.
Test your understanding of the three logarithm rules discussed in this section.
Learn what the change of base rule says, how to memorize it and prove why it is true.
Discover what the number e means and learn the notation for one of the most-used logarithms: the natural logarithm.
Be able use your calculator to find the logarithm of any positive number in any base!
Practice examples using the change of base rule, the natural logarithm, and calculating logarithms using the change of base rule to convert to base 10 or base e.
Test your understanding of the change of base rule and the natural logarithm.
Understand the domain and range of a given function.
Learn how to graph a function which has been transformed by: being vertically or horizontally shifted, vertically or horizontally stretched or shrunk, or reflected in the x-axis or y-axis.
Understand what makes a function one-to-one and how to check for this using the horizontal line test. Learn what the inverse function is and how to visualize it graphically.
Learn the general shape and behaviour of an exponential function so that you can graph transformations of these functions with ease.
Learn the general shape and behaviour of a logarithmic function so that you can graph transformations of these functions with ease. Understand the graphical relationship between a logarithmic function and an exponential function.
Test your understanding of the graphs of exponential and logarithmic functions.
Learn how to solve an exponential equation by using either the one-to-one property of exponential functions or by following 3 simple steps which make use of logarithms.
Learn how to handle more advanced exponential equations.
Practice solving exponential equations.
Learn how to solve a logarithmic equation by using either the one-to-one property of logarithmic functions or by following 3 simple steps which make use of exponents.
Practice solving logarithmic equations.
Test your understanding of how to solve exponential and logarithmic equations.
Understand three common uses of a logarithmic scale in daily life: the pH scale, the decibel scale and the Richter scale.
Given an equation for one variable in terms logarithmic or exponential equation of a second variable, be able to solve for the second variable in terms of the first.
Use logarithms to solve exponential equations related to compound interest.
Review what you have learned in this course and think about where to go from here.
Test your understanding of how to apply logarithms in real life.
I have a PhD in mathematics from The University of Queensland and I'm currently a Postdoctoral Research Fellow in the field of graph theory and combinatorics. I also have a BSc and a MSc in mathematics from The University of Victoria. As an aside, I have a black belt in Shotokan karate :)
I've tutored and taught mathematics at university. The thing I love the most about teaching math is when students who thought they couldn't do math come to me and say that they can understand it now and they also ENJOY it. It's great to share my enthusiasm for math with others.