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# Pre-Cal 40S April 17, 2009

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Introduction to logarithm laws.

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### Pre-Cal 40S April 17, 2009

1. 1. Don't forget ... a logarithm is an exponent! ... if you do you may get mud on your face. Pararescue by ﬂickr user slagheap
2. 2. Let's see 2^x Then, sketch the graph of it's inverse ...
3. 3. Sketch the given function AND it's inverse on the graph.
4. 4. Rewrite each table of values for the inverse of each function ...
5. 5. The Anatomy Of A Power exponent 3 2 = 8power base power EXPONENTIAL FUNCTIONS turn EXPONENTS into POWERS
6. 6. a b=c log b c = a b is the base b is the base a is the exponent a is the (exponent) logarithm c is the power c is the (power) argument These functions are inverses of each other. EXPONENTIAL FUNCTIONS LOGARITHMIC FUNCTIONS turn EXPONENTS into POWERS turn POWERS into EXPONENTS
7. 7. a b=c log b c = a b is the base b is the base a is the exponent a is the (exponent) logarithm c is the power c is the (power) argument A Logarithm is an Exponent you're going to forget that
8. 8. Graph the function (a) Is there an asymptote? If so state its equation. If not, explain why not. (b) State the domain. (c) State the range. (d) Is the function increasing or decreasing. Explain.
9. 9. Simplify . The Product Law
10. 10. Simplify The Quotient Law
11. 11. Simplify The Power Law
12. 12. 3 log2 8 = log2 2 = In General ... x log5 5 = x loga a = x x log7 49 = loga a =
13. 13. log 39 =9 3 In General ... log ax =x log 710 a = 7