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Logarithms and Exponents Teacher Resources
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Learners are given a logarithmic function and its inverse exponential function. The task, which is to graph both compositions of the two functions, uses the inverse nature of exponents and logarithms to generalize about the properties of any two inverse functions. This activity is the second in a series of two. Note that the resource itself references only Common Core standard F-BF.4. This review, however, includes Common Core standard F-BF.5 because the task is very dependent on understanding the inverse relationship between exponents and logarithms.
This task focuses on using the verbal definition of the logarithm to understand that a logarithm is an exponent. Learners complete six computational exercises using the inverse properties of logs and exponents and answer two discussion questions about generalized cases. This activity is the first in a series of two.
Sal gets to the heart of the matter in this video, clarifying that it's important to understand math "so you can actually apply it in life later on and not have relearn everything every time." True to his word, Sal demonstrates ways to more easily and intuitively solve logs and exponents with several well-explained examples.
Exponential functions are the name of the game. Young mathematicians can work through each of the eight worksheets by evaluating functions, applying logarithms, completing logarithmic functions, and building inverse functions. This would be a great set of worksheets to accompany an entire chapter.
Algebra scholars read about and practice problems involving exponents. They solve problems by using common exponential rules for multiplying and dividing exponents. They use prior knowledge of logarithms to solve exponential problems. Each of the three lessons in this unit includes a detailed explanation and a set of practice problems. Answers are included at the end of the packet.
Students solve exponential equations using logarithms. In this solving exponential equations using logarithms lesson, students read a story on their Ti-Nspire about exponentials and logarithms. Students solve problems in the story using logarithms. Students use the power, product, and quotient properties to solve the stories' problems.
Learners explore the characteristics of logarithmic functions and their relationship to exponential functions. Using the subscriber website Explorelearning.com, pupils observe changes in the input variable and its effect on the graph of the functions, examine reflections over the line y = x, and examine the restrictions associated with each function. Explore the compound interest equation as a real world application.