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5.5 Logarithms

5.5 Logarithms. 5.5 Logarithms. Objectives: I will be able to… Rewrite equations between exponential and logarithmic forms Evaluate logarithms Solve logarithms Vocabulary: logarithms, natural logarithms. Why learn about logarithms?. 5.1-5.4 were all about exponents

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5.5 Logarithms

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  1. 5.5 Logarithms

  2. 5.5 Logarithms Objectives: I will be able to… • Rewrite equations between exponential and logarithmic forms • Evaluate logarithms • Solve logarithms Vocabulary: logarithms, natural logarithms

  3. Why learn about logarithms? • 5.1-5.4 were all about exponents • A logarithm is the inverse of an exponent • We can use logarithms to solve for a missing exponential value

  4. Logarithmic Function exponent x and b are ALWAYS POSITIVE y can be + or - We discovered last week that exponential functions followed the same translation rules as polynomials. We can switch between these two forms to assist us in solving problems. number base

  5. Rewrite Exponents ⟶ Logs x = 216 b = 6 a=3 x = .01 a=-2 b = 10 x = .0498 a=-3 b= e

  6. Logarithmic Function Solve for the missing variable by changing to exponential form.log5 c = 3 loga64 = 2 log7= w c 64 125 c a ± 8 w -2

  7. Logarithmic Function Two special types of logarithms: • Common Log  • No b means base 10 • Natural Log  • ln means base e

  8. Logarithmic Function =y .01 -2 Evaluate: If not an equation, let log equal y as in general form. No base means base 10. Evaluate: =y =y =y e 10 y Remember number and base can not be negative. y

  9. Logarithmic Function Solve for x using logarithm and exponent rules. Change form of logarithm. Change form of 729. Use exponent rules. Not matching exponents, must get rid of exponent with x.

  10. Homework pg. 194 #1-7 odd, 12, 14, 17

  11. Exit Ticket 1. Rewrite the following log functions into exponential form: a) b) • Solve for x. a) b)

  12. Homework- Day 2 pg. 196-197 #36-42 even, 47

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