Download Solving Exponential Functions: Common Base

Logarithmic Functions
Today’s Objective:
I can write and evaluate logarithmic expressions.
4 different ways
64 = 641
= 82
= 43
= 26
5 different ways
4096 = 40961
= 642
= 163
= 84
= 46
= 212
7 different ways
16,777,216 = 167772161
= 40962
= 2563
= 644
= 166
= 88
= 412
= 224
Solving exponential equations using common bases
5𝑥
= 125
Write each side with
the same base.
𝑥
5 =5
3
Since bases are the same
exponents must be equal.
𝑥=3
1
𝑥
4 =
16
4𝑥
=
1
4
2
4𝑥 = 4 −2
𝑥 = −2
4𝑥 = 32
22𝑥 = 25
2𝑥 = 5
5
𝑥=
2
2𝑥 = 7
Exponential & Logarithm Equations
Exponential
Equation
ab
Logarithm
Equation
Exponent/power
Inverse
x
logb a  x
𝑏
log𝑏 𝑎
= 𝑎
log 𝑏 𝑏 𝑎 = 𝑎
Base
Result
Read: log base b of a
Common Log:
Logs with a base 10
Written log only – no base # needed
Calculator button: [LOG]
𝑎=
Write in
logarithmic form
14 = 5𝑥
23 = 𝑒 𝑥
𝑏
𝑥
↔ log 𝑏 𝑎 = 𝑥
log 5 14
14 = 𝑥
log 𝑒 23 = 𝑥
6 = 103𝑥+1
log10 6 = 3𝑥 + 1
log 6 = 3𝑥 + 1
Write in
exponential form
𝑥
𝑥
3 =
log 3 8 = 𝑥
3
8
52𝑥 = 34
log 5 34 = 2𝑥
log 8 (6) + 1 = 𝑥
log 8 6 = 𝑥 − 1
8𝑥−1 = 6
Solve each equation by using common
base method
𝑥 = log 5 625
5𝑥 = 625
5𝑥 = 5 4
𝑥=4
𝑎 = 𝑏 𝑥 ↔ log 𝑏 𝑎 = 𝑥
log 3 27 = 𝑥 − 7
3𝑥−7 = 27
3
𝑥−7
=3
3
𝑥−7=3
𝑥 = 10
log 4 64 = 2𝑥 + 3
42𝑥+3 = 64
42𝑥+3
3
=4
2𝑥 + 3 = 3
𝑥=0