Knowing how to simplify and evaluate Logarithmic Functions is not only important in Pre-Calculus, but it is what gives students the edge in Calculus and beyond!
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Logarithms are the inverse operation of exponential functions, just like addition is the inverse operation of subtraction, and there are only 9 basic Properties that are so super easy to learn!
First, we will walk ourselves through the nine properties, and see how they are used in proving the definition of a logarithm.
And then we will see all properties for
- Common Logarithm (base 10)
- Natural Logarithm (base e)
Then we will learn how to expand a logarithm by writing it as a sum, difference or product.
Property of Logarithms
Next we will condense logarithmic expressions by writing each expression as a single logarithm.
Gosh, what’s so cool, is that these properties fit so easily together, and are straightforward and painless to apply.
Why?
Exponential and Logarithmic Property
Because they are inverses, and they are used to change from an exponential equation to a logarithmic equation and vise versa, depending on what the question requires.
Lastly, we will look at the Change of Base Formula. As Paul’s Online Notes nicely states, most calculators are only capable of evaluating either common logarithms and natural logarithms.
So what do you do if you need to evaluate another log that isn’t base 10 or base e?
Thankfully, the Change-of-Base Theorem allows us to take any logarithm with any base and turn it into either the common or natural logarithm.
Awesome!
Logarithmic Functions – Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.