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Warm Up

Warm Up. Factor Completely. 25x 2 – 36 8x 3 + 27 x 2 + 5x – 14 14y 2 – 33y – 5 x 3 – 4x 2 + 5x – 20. Evaluating Logs ( ln ) & Properties of Logs. Logarithms… Log functions and exponential functions are inverses… If f(x) = b x ,then f -1 (x) = log b x.

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Warm Up

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  1. Warm Up Factor Completely. 25x2 – 36 8x3+ 27 x2 + 5x – 14 14y2 – 33y – 5 x3 – 4x2 + 5x – 20

  2. Evaluating Logs (ln) & Properties of Logs

  3. Logarithms… Log functions and exponential functions are inverses… If f(x) = bx,then f-1(x) = logbx

  4. Logarithmic Form Exponential Form Lots of examples of switching forms…

  5. Talk to your group… • If 101.681 = 48, what is log 48 ? _____ • If log 156 = 2.193, what is 102.193 ? __

  6. Your Turn… Log864 = ____ Log464 = ____ Log264 = ____ Log6464 = ____ Log81 = ____ Log8 (1/64) = ____

  7. If 52.892 = 105, then log5105 = ____ • If log217 = 4.088, what is 24.088 ? • log5(54) = ____ • = ____

  8. Ln (read “Natural Log”) is a special log with a base e. Basic Log Properties: • ln 1 and log 1 = _____ • lne = _____ • logbb = _____ • elnx = _____ • _____

  9. Rules for Logs

  10. Examples: Use the properties of logs to expand. Write as a single log(condense):

  11. Change of Base • Since our calculators can only evaluate a base of 10 or e, we will let a = 10 or use ln. • This formula allows us to evaluate logs with ANY base using the calculator!

  12. Examples Evaluate using change of base:

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