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After reading this text and / or viewing the video tutorial on this topic you should be able to: explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms.
Logarithms and Logarithmic 6.3 Functions. Essential Question. What are some of the characteristics of the graph of a logarithmic function? Every exponential function of the form f (x) bx, where b is a positive real number. = other than 1, has an inverse function that you can denote by g(x) = logb x.
These logarithmic worksheets are designed to guide students from basic to advanced concepts, providing a step-by-step progression that encourages confidence and competence. For teachers, the collection offers a ready-made resource to assign homework or in-class practice, saving time and ensuring comprehensive coverage of logarithmic topics.
In this unit we look at how we can use logarithms to simplify certain functions before we di er- entiate them. To start o , we remind you about logarithms themselves.
LOGARITHMS PRACTICE SIMPLIFYING EXPRESSIONS. single logarithm. log 2 7 + log 2 2. log 2 20 − log 2 4. 3log 5 2 + log 5 8. 2log 6 8 − 5log 6 2. log 10 8 + log 10 5 − log 10 0.5. log 2 14 , log 2 5 , log 5 64 , log 6 2 , log 10 80. single logarithm.
Having previously defined what a logarithm is (see the notes on Functions and Graphs) we now look in more detail at the properties of these functions. The relationship between logarithms and exponentials is expressed as:
6 x − log 6 (x − 6) = 1 22) log 6 x − log 6 (x + 6) = 1 23) log 4 8 − log 4 (x + 6) = 1 24) log 3 x − log 3 (x + 5) = 3 Review: Simplify. Your answer should contain only positive exponents. 25) 2y2 ⋅ (2x4y4) 4 x2y4 26) (2n−4) 3 ⋅ (2m2n4) 2 (2m4n4) 4 Review: Condense each expression to a single logarithm. 27) log 7 x 3 + log 7 y ...
