4.2: Logarithmic Functions
1.
Convert to exponential form:
a) 2 = log 7 𝑥
b) 3 = log 𝑦 27
c) log 4 64 = 𝑦
2.
Convert to logarithmic form:
a) 34 = 𝑥
b) 𝑦 3 = 8
c) 𝑒 𝑥 = 10
3.
Evaluate the logarithmic expression.
a) log 2 8
b) log 4 16
c) log 3 81
d) log 5 125
e) log 4
1
f) log 6
1
4
36
g) log 64 8
7
h) log 3 √3
i) log 1 4
2
j) log 1
3
1
27
k) log 2 −1
4. Evaluate the logarithmic expression.
a) log17 17
b) log 8 1
c) log 3 35
d) 7log7 13
5. Graph the two functions on the same axes
a. 𝑓(𝑥 ) = 2𝑥 and 𝑔(𝑥 ) = log 2 𝑥
b. 𝑓(𝑥 ) = 3𝑥 and 𝑔(𝑥 ) = log 3 𝑥
What is the relationship between 𝑦 = 𝑏 𝑥 and 𝑦 = log 𝑏 𝑥?
6.
Graph the logarithmic function one step at a time, starting
with the parent function.
a) 𝑓(𝑥 ) = 2 log 2 𝑥 − 3
1
b) 𝑓(𝑥 ) = − log 2 ( 𝑥)
3
Domain
In general, the domain of 𝑓(𝑥 ) = log 𝑏 𝑔(𝑥) consists of all 𝑥
such that 𝑔(𝑥) > 0
7. Find the domain of each logarithmic expression
a) 𝑓(𝑥 ) = log 5 (𝑥 + 4)
b) ℎ(𝑥 ) = log 9 (1 − 2𝑥 )2
c) 𝑓(𝑥 ) = log 2 (𝑥 2 + 7𝑥 + 12)
The Common Logarithm and The Natural Log
 A logarithm with base 10 is called the common log.
 A logarithm with base 𝑒 is called the natural log.
8. Evaluate:
a) log 10,000
b) log 1015
c) log 1
d) ln 𝑒
e) ln
1
𝑒4
f) 10log 47
g) 𝑒 ln √𝑥
9.
Graph the logarithmic function one step at a time, starting
with the parent function: 𝑓(𝑥 ) = 2ln⁡(−𝑥)