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Unformatted text preview: Name___________________________________ 3.4: Logarithms and Logarithmic Scales
Properties of Logarithms In the following properties, b, M, and N are positive real numbers (b 1). Product Property logb (MN) = logb M + logb N Quotient Property logb M = logb M  logb N N Power Property logb (Mp) = p logb M Logarithmofeachside property M = N implies logb M = logb N Onetoone property logb M = logb N implies M = N Examples: log5 (2x) = log5 2 + log5 x log4 1 = log4 1  log4 16 16 = 0  2 = 2 1. Use the properties of logarithms to expand the given logarithm in terms of logarthims of x, and y. log5 x y
3 2. Use the properties of logarithms to expand the given logarithm in terms of logarthims of a, b, and c. a3b2 c log2 NOTE: logb (M + N) logb M + logb N That is, logb (M + N) cannot be expanded. Use the properties of logarithms to rewrite the expression as a single logarithm with a coefficient of 1. 3. 5 log4(x  7)  3 log4x 1 4. 9 log x + log y + log (z + 3) 2 5. ln x 2  25  ln (x + 5) (Hint: Cancel any common factors, when appropriate.) Change of Base Formula If x and b are positive real numbers and b 1, then logb x = log x ln x = log b ln b Use the change of base formula to evaluate the log. Round to the nearest ten thousandth (four decimal places). 6. log8 85 7. log3 14 15 Refer to page 246 in your textbook to answer the following questions regarding the Richter scale magnitude of an earthquake. 8. Find the intensity of an earthquake measuring 8.7 on the Richter scale. Refer to page 250 in your textbook to answer the following questions regarding the pH scale. 9. Lye has a hydroniumion concentration of 3.67 10 whether it is an acid or base.
14 mole per liter. Determine the pH of lye and state Graph the function by making a table of points. The state the domain and range of the function. (Hint: Replace f(x) with y. Then convert the logarithmic equation to its exponential form and solve for x.) 10. f(x) = log (x + 2)  1 3
y 6 4 2 x y 2 1 0 1 2 6 4 2 2 2 4 6 x 4 6 Domain: ________________________________ Range: __________________________________ Answer Key Testname: 3.4 LOGARITHMS AND LOGARITHMIC SCALES 1 1. log5 x + log5 y 3 1 2. 3log2 a + 2log2 b  log2 c 2 (x  7)5 x3 3. log4 4. log x 9 y z + 3 5. ln (x  5) 6. 2.1365 7. 0.0628 8. 501,187,233 I0 9. 13.4; base 10.
y (7, 1) (1, 0) (1, 1) (1.67, 2) x Domain = (2, ) Range = all real numbers ...
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This note was uploaded on 04/13/2008 for the course MATH 2412 taught by Professor Matroy during the Spring '08 term at Alamo Colleges.
 Spring '08
 MatRoy
 Real Numbers

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