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Solving Exponential Equations

Solving Exponential Equations. What is to be learned?. How to solve exponential equations. Exponential Equation?. Equation where power is unknown 5 x = 125 x = 3 3 x = 20 x = 2.73. (General Knowledge). (Trial and error). need a better tactic. The Log Tactic.

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Solving Exponential Equations

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  1. Solving Exponential Equations

  2. What is to be learned? • How to solve exponential equations

  3. Exponential Equation? Equation where power is unknown 5x = 125 x = 3 3x = 20 x = 2.73 (General Knowledge) (Trial and error) need a better tactic

  4. The Log Tactic 8x = 900 neat wee tactic log 8 = log 900 x = log 900 log log x log 8 x = 3.27

  5. A bit nastier 15 X 3x = 3000 3x = 3000 3x = 200 log 3x = log 200 x log 3 = log 200 x = log 200 x = 4.82 15 log 3

  6. Solving Exponential Equations Equations where unknown is a power

  7. 30 X 6x = 1200 Eliminate 30 6x = 1200 6x = 40 Logs on both Sides Log 6x = log 40 Neat wee tactic x log 6 = log 40 x = log 40 30 (using log10) = 2.06 log 6

  8. Natural Growth P is Population over t days Population of some sort of creepy crawlie P = P0e0.2t If there are 1000 ccs to start with, how long will it take to reach a million? 1000000 = 1000e0.2t 1000000 = e0.2t 1000 = e0.2t ln 1000 = ln e0.2t ln 1000 = 0.2t ln e P0 P ln 1000 = 0.2t 1000 t = ln 1000 0.2 = 34.5 days = 1

  9. When e is involved using ln is a neat tactic Tina’s tea temperature (T 0C) after t mins T = T0e-0.2t How long until it is half its initial temp? T = e-0.2t 0.5 = e-0.2t ln 0.5 = ln e-0.2t ln 0.5 = -0.2t ln e ln 0.5 = -0.2t t = ln 0.5 T0 = 1 = 3.5 mins -0.2

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