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Today in precalculus

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- Go over homework
- Notes: Solving Exponential Equations
- Homework

- Isolate the term with the variable exponent using algebra.
- Take the log of both sides (or convert to a log equation)
- Use properties of logs
- Solve for the unknown.

5x = 358

log5x =log358

xlog5=log358

x = 3.654

3ex - 6 = 48

3ex = 54

ex = 18

lnex= ln18

x=ln18

x = 2.890

x = -1.839

2. 6e2x + 10 = 46

6e2x = 36

e2x = 6

2x = ln6

x = .896

3. 10e-x + 45 = 83

10e-x = 38

e-x = 3.8

-x = ln3.8

-x = 1.335

x = -1.335

ex + 2e-x = 3

ex + 2e-x – 3 = 0

ex(ex + 2e-x – 3 = 0)

e2x – 3ex + 2e0 = 0

e2x – 3ex + 2= 0

(ex – 2)(ex – 1) = 0

ex = 1 ex = 2

x = ln1 x = ln2

x = 0, .693

ex – e-x = 10

ex – e-x – 10 = 0

ex(ex– e-x – 10 = 0)

e2x – 10ex – e0 = 0

e2x – 10ex– 1 = 0

ex = 10.099 ex = -.099

x = ln10.099 x = ln(-0.099)

x = 2.312

- Page 331: 1-6, 11-16, 29-33
- Quiz Friday, January 10