1. Today in Precalculus Go over homework
Notes: Solving Exponential Equations
Homework

2. Steps to Solving Exponential Equations
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.

3. Example
5x = 358
log5x =log358
xlog5=log358
x = 3.654

4. Example
3ex - 6 = 48
3ex = 54
ex = 18
lnex = ln18
x=ln18
x = 2.890

5. Practice

6. x =

7. 2. 6e2x + 10 = 46
6e2x = 36
e2x = 6
2x = ln6
x = .896

8. 3. 10e-x + 45 = 83
10e-x = 38
e-x = 3.8
-x = ln3.8
-x = 1.335
x =

9. 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

10. x =( log10.099)/(log2) or x = (log-0.099)/(log2) x = 3.336
2x – 2-x = 10
2x – 2-x – 10 = 0
2x(2x– 2-x – 10 = 0)
22x – 10(2x)– 20 = 0
22x – 10(2x ) – 1 = 0
2x = or 2x = -.099
x =( log10.099)/(log2) or x = (log-0.099)/(log2)
x = 3.336

11. Homework
Page 331: 1-6, 11-16, 29-33
Quiz Friday, January 8