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Today in Pre-Calculus

Today in Pre-Calculus. Go over Friday’s assignment Review Chapter 3 Homework. Converting to logs. Example: 16 = 4 x Example: 17 = 3 x Example: 183 = e x. Converting to exponents. Example: 3 = log 4 x Example: 4 = log 5 x Example: ln x = 2. Change of Base Formula.

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Today in Pre-Calculus

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  1. Today in Pre-Calculus • Go over Friday’s assignment • Review Chapter 3 • Homework

  2. Converting to logs • Example: 16 = 4x • Example: 17 = 3x • Example: 183 = ex

  3. Converting to exponents • Example: 3 = log4x • Example: 4 = log5x • Example: lnx = 2

  4. Change of Base Formula Allows us to rewrite logs in terms of base 10 or e so we can calculate the value of the log. Example: Find the value log428

  5. Properties of Logs log10= lne= log10x= lnex= log1= ln1= 10logx = elnx =

  6. Condensing Log Expressions Example: condense: log5x - log5y Example: Condense: 3lnx + 4 ln(y+4)

  7. Expanding Log Expressions • Use the properties of logs to rewrite one log expression into multiple log terms. example: Expand log812y

  8. Solving exponential Equations

  9. Solving Log Equations Example 1: log(4x + 2) – log(x – 1) = 1 Example 2: ln(x – 2) + ln(2x – 3) = 2lnx

  10. Interest • Compound interest: • Continuously Compounded interest: A=Pert A: final amount P: principal r: interest rate k: number of payments per year t: number of years

  11. Example How long will it take for an investment of $15,000 to grow to $27,000 if interest is compounded quarterly with a 7.5% interest rate? How long will it take if the interest is compounded continuously?

  12. Graphs y = 2x

  13. Transformations y = 2x+2

  14. Transformations y = -2x

  15. Homework • Pg 286: 25-30all • Pg 308: 17-23 odd • Pg 317: 7-11odd, 15-21odd, 23-27odd • Pg 331: 11-15odd • Pg 341: 21-27odd • Pg 345: 31,32,53,54

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