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Solve each equation for x. 3x – 12 = 45 x = 19 2.

Algebra 3 Warm-Up 5.3. Solve each equation for x. 3x – 12 = 45 x = 19 2. . x = 39.2. Algebra 3 Lesson 5.3 Objective: SSBAT write and evaluate logarithmic expressions. Standards: 2.1.11A. Review: Addition and Subtraction are opposite operations .

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Solve each equation for x. 3x – 12 = 45 x = 19 2.

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  1. Algebra 3 Warm-Up 5.3 • Solve each equation for x. • 3x – 12 = 45 • x = 19 • 2. x = 39.2

  2. Algebra 3 Lesson 5.3 Objective: SSBAT write and evaluate logarithmic expressions. Standards: 2.1.11A

  3. Review: Addition and Subtraction are opposite operations. Multiplication and Division are opposite operations. Squaring and Square Rooting are opposite operations.

  4. Solve for x. • 3x= 19683 • You could use guess and check or you can use logarithms. • Logarithms are the opposite of Exponential functions.

  5. Logarithmic Equation • An equation of the form x = logby • y is a positive number  Used to solve exponential equations • logb y is read as “log base b of y”

  6. Exponential Form To Logarithmic Form y= bx x= logby ** The base of the Exponent becomes the base of the Logarithm. ** The exponent is all by itself in the logarithm.

  7. Write each in Logarithmic Form 1. 53 = 125 3 = log5 125 5 = log4 1024 2. 45 = 1024 2401 log7 m = 3. 7m = 2401 4 = log12 20736 4. 20736 = 124

  8. 5. 100 = 1 0 = log10 1 6.

  9. Change each to Exponential Form • log515625 = 6 • 56 = 15625 • log2 128 = 7 • 27 = 128

  10. Change each to Exponential Form 3. logx2048 = 5.5 x5.5= 2048 4. = ½

  11. Common Logarithm • A logarithm that has a base of 10 • log10 y • You can write it as log y - When there is no base shown it is base 10  log10 15 = log 15  Common Logarithms are used to measure pH (acidity), decibels (sound), Richter Scale (earthquakes)

  12. Since the Common Logarithm log10 is used the most in real world applications it is given a key on the calculator. • Evaluate each. • log10 150 • log 240 • 3. log -13 = 2.176 = 2.380 Undefined

  13. Change of Base Property • Used to evaluate non base 10 logarithms in your calculator.  For any positive number M and b, with b ≠ 1 logbM =

  14. Evaluate log2 32 log (32) log (2) = 5

  15. Evaluate each. • log8 16 = 4/3 or 1.333…

  16. log9 27 3. = 1.5 = -.83333

  17. log4 (-600) Answer: Undefined (cannot take the log of a negative number)

  18. On Your Own. • Change to Logarithmic Form • Change to Exponential Form • 3. Evaluate. Show the change of base form. log81 3 = ¼  811/4 = 3 log2 8

  19. Homework Worksheet 5.2

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