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Student Practice 9
Evaluate.
(a)
log
7
1
(b)
log
8
8
(c)
Find
y
if log
12
13 = log
12
(
y
+ 2).
We now have the mathematical tools needed to solve a variety of logarithmic equations.
EXAMPLE 10
Find
x
if 2 log
7
3
−
4 log
7
2 = log
7
x
.
Solution
We can use property 3 in two cases.
By substituting these results, we have the following.
log
7
9
−
log
7
16 = log
7
x
Student Practice 10
Find
x
if log
3
2
−
log
3
5 = log
3
6 + log
3
x
.
744745
12.3 Exercises
Express as a sum of logarithms.
1.
log
3
AB
2.
log
12
CD
3.
log
5
(7
· 11)
4.
log
6
(13 · 5)
5.
log
b
9
f
6.
log
b
5
d
Express as a difference of logarithms.
7.
8.
9.
10.
11.
12.
Express as a product.
13.
log
8
a
7
14.
log
3
c
8
15.
log
b
A
−
2
16.
log
a
B
−
5
17.
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18.
Mixed Practice
Write each expression as a sum or difference of logarithms of a single variable.
19.
log
8
x
2
y
20.
log
6
xy
4
21.
22.
23.
24.
25.
26.
Write as a single logarithm.
27.
log
4
13 + log
4
y
+ log
4
3
28.
log
8
15 + log
8
a
+ log
8
b
29.
5 log
3
x
−
log
3
7
30.
3 log
8
5
−
log
8
z
31.
32.
745746
Use the properties of logarithms to simplify each of the following.
33.
log
3
3
34.
log
7
7
35.
log
e
e
36.
log
10
10
37.
log
9
1
38.
log
e
1
39.
3 log
7
7 + 4 log
7
1
40.
Find x in each of the following.
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