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ET 5.5

ET 5.5. Use change of base to rewrite the expression as a quotient of two logarithms with base e, 10, & 7. Base e. Base 10. Base 7. Two types of exponential functions you can face…. Note: If the exponential problem doesn’t look like this you can force it to.

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ET 5.5

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  1. ET 5.5 Use change of base to rewrite the expression as a quotient of two logarithms with base e, 10, & 7. Base e Base 10 Base 7

  2. Two types of exponential functions you can face… Note: If the exponential problem doesn’t look like this you can force it to.

  3. Two types of log functions you can face… log(3x) = log(15) log2x = -4 x = 2-4 3x = 15 x = 5 x = 1/16 Note: If the log problem doesn’t look like this you can force it to.

  4. How many ways can you come up with to solve… 3x+5 = log226 23x+5 = 64 3x+5 = 6 23x+5 = 26 x = 1/3 3x+5 = 6 x = 1/3 ETC.

  5. We already know. What about y = 7x Since we know something about the derivative when the base is e, let’s rewrite this so that the base in in terms of e. log7y = x Pattern lny = (ln7) x y = e(ln7)x y’ = e(ln7)x(ln7) y’ = (ln7) 7x

  6. What we knew before:What we now know:Combine the two:

  7. Find y’. y = 23x y’ = (ln 2) 23x (3) y’ = (3ln 2) 23x

  8. Assignments 5.5 • Day 1: 1 - 49 odd • Day 2: Day 2: 42 - 48 even, 51 -61 odd, 63, 67, 71, 75-85 odd, 87, 88, 89, 92-94

  9. Find y’. Pattern Product Rule

  10. What we knew before:What we now know:Combine the two:

  11. Find y’

  12. Not including trig functions, here is everything we know about derivatives. Variable base Variable expo.

  13. Find y’ Variable expo. & base

  14. Summary of integration not including trig functions.

  15. Assignments 5.5 • Day 1: 1 - 49 odd • Day 2: 42 - 48 even, 51 -61 odd, 63, 67, 71, 75-85 odd, 87, 88, 89, 92-94

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