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Today in precalculus
• Go over homework
• Notes: Solving Exponential Equations
• Homework
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.
Example
5x = 358
log5x =log358
xlog5=log358
log 358
x
log 5
x = 3.654
Example
3ex - 6 = 48
3ex = 54
ex = 18
lnex = ln18
x=ln18
x = 2.890
Practice
x
1.
2.
3.
1
5    64
4
2x
6e  10  46
x
10e  45  83
x
1
1. 5    64
4
x
1
   12.8
4
x
1
log = log12.8
4
log12.8
x
1
log
4
x = -1.839
2. 6e2x + 10 = 46
6e2x = 36
e2x = 6
2x = ln6
ln 6
x
2
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
e x = 1 ex = 2
x = ln1 x = ln2
x = 0, .693
e e
2
x
x
5
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
Homework
• Page 331: 1-6, 11-16, 29-33
• Quiz Friday, January 8