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12.5/12.7 Solving Exponential and Logarithms

12.5/12.7 Solving Exponential and Logarithms . Brett Solberg AHS ’11-’12. Warm-up. 1) Expand the Logarithm 2) Simplify the expression to one logarithm Have your HW out for stamps and questions You need a scientific calculator!. Quiz Retakes. Courtney, Josi, Rachel, Arthur.

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12.5/12.7 Solving Exponential and Logarithms

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  1. 12.5/12.7 Solving Exponential and Logarithms Brett Solberg AHS ’11-’12

  2. Warm-up • 1) Expand the Logarithm • 2) Simplify the expression to one logarithm • Have your HW out for stamps and questions • You need a scientific calculator!

  3. Quiz Retakes Courtney, Josi, Rachel, Arthur

  4. Today’s Agenda • 12.5 • Calculating Logarithms and Antilogarithms • 12.7 • Solving Exponential and Logarithmic Equations • Solving Interest and loudness formulas

  5. Common Logarithms • A logarithm with base 10 is a common logarithm. • We can easily calculate common logs using a calculator.

  6. Common Logarithms • log 7.09 • log 4.00 • log 9.99

  7. Antilogarithm • Common Logarithm • 7 = x 10x = 7 • Antilogarithm 107 = x • antilog4.3425

  8. Antilogarithm antilog 3.0098 = antilog – 3.0067 = antilog -6.7628 = antilog 4.8069 = antilog(6.6284-10) =

  9. Review • Solve for x • = 4 • x2 + 2 = 11 • Square cancels a square root • Square root cancels square

  10. Solving Exponential Equations • You get variables out of equations using logs • 5x = 7 35x – 2 = 8

  11. Solving Exponential Equations 35x – 2 = 27 4x = 6 42x – 3 = 64

  12. Solving Logarithmic Equations • we eliminate logs by raising both sides by its base • 4

  13. Solving Logarithmic Equations log(x – 1) + log(x + 1) = 1 logx + log(x + 3) = 1

  14. Annual Compound Interest Principle Amount time (years) rate (decimal) Resulting Amount A = P(1 + r)t

  15. Interest A = P(1 + r)t Suppose $5,000 was invested at 14%, compounded annually, and it yielded $18,540. For how long was it invested?

  16. Interest A = P(1 + r)t Suppose $1,000 is invested at 8%, compounded yearly. How long will it take for the investment to grow to $2,000?

  17. Loudness Intensity minimal intensity Loudness (bells)

  18. Loudness Find the loudness in decibels of the sound in a library for which the intensity is 2510 times

  19. Loudness Find the loudness in decibels of conversational speech for which the intensity is 106 times

  20. Homework 12.7 pg 547 1 – 27 all, skip 22 and 23

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