Name: _____________________________________ Period: ____ Date: ___________________
3.2 – 3.3 Logarithmic Functions Review
Expand each logarithm.
Condense each expression into a single logarithm.
Rewrite each equation in exponential form.
Rewrite each equation in logarithmic form.
Expanding Logarithmic Expressions
Write each of the following as the sum or difference of logarithms. In other words, expand
each logarithmic expression.
A) log 2
3x3 y 2
z5
B) log 3 5 3 xy 2
3
C) log 4 ( x + 1) ( x − 2 )
5
E) log 2
3( x + 2)
x −1
G) log a 12 x 3 y
2
D) log 5
6x2
11 y 5 z
3
F) log12
H) log 3
x−7
x+2
5x5 y3
3
z2
Condensing Logarithmic Expressions
Rewrite each of the following logarithmic expressions using a single logarithm. Condense
each of the following to a single expression. Do not multiply out complex polynomials. Just
3
leave something like ( x + 5 ) alone.
1
B) 2 log x + log y
2
A) 3log 4 x − 5log 4 y + 2log 4 z
1
1
2
log 6 + log x + log y
3
3
3
D)
3
1
log 3 16 − log 3 x 3 − 2 log 3 y
4
3
E) 3log 5 x + 2 log 5 y + log 5 z + 2
F)
1
2
log 2 x + log 2 y − 3
3
3
G) log 3 ( x + 2 ) + log 3 ( x − 2 ) − log 3 ( x + 4 )
H)
2
1
1
log ( x + 1) + log ( x − 2 ) − log ( x + 5 )
3
3
3
C)
Practice Using Properties of Logarithms
Use the following information, to approximate the logarithm to 4 significant digits by using
the properties of logarithms.
log a 2 ≈ 0.3562,
A) log a
6
5
D) log a 30
G) log a
4
9
log a 3 ≈ 0.5646,
and
log a 5 ≈ 0.8271
B) log a 18
C) log a 100
E) log a 3
F) log a 75
H) log a 3 15
I) log a 542
For each equation:
a) Explain the transformation.
b) State the domain and range (in interval notation).
c) State the vertical asymptote.
d) Describe the end behavior.
e) Increasing or decreasing?
21)
22)
23)
24)
25)
26)
27)
28)
29)
Word Problems:
3-2: #26, 27, 42, 55, 68
3-3: #17, 18, 59, 60, 75, 98, 103, 112
30)