Name:
Answer Key
Period: ______
Algebra II
Review – Logarithms and Inverse Relations
Expand the expression.
1)
log 6 3x
2)
log 6 3 + log 6 x
4)
xy
log 4
3
5)
log 2
x
5
3)
log 2 x − log 2 5
log x + 2log y
log5 2 x
x2 y
log 2
z
6)
1
log 5 2 + log 5 x
2
log 4 x + log 4 y − log 4 3
log xy 2
2log 2 x + log 2 y − log 2 z
Condense the expression.
7)
log 3 7 − log 3 x
log 3
9)
8)
7
x
log 5 3x 2
1
log x − log 4
2
log
2log5 x + log5 3
10)
x1 2
x
or log
4
4
log 3 4 + 2log 3 x − log 3 5
log 3
4x 2
5
Rewrite the following in exponential form.
11)
log 3 12 = x
12)
3 x = 12
log 3 x = 4
13)
34 = x
log x 2.8 = 5
x 5 = 2.8
Rewrite in logarithmic form.
14)
74 = x
log 7 x = 4
15)
e x = 45
log e 45 = x or ln 45 = x
16)
x14 = 19
log x 19 = 14
Solve. Check for extraneous solutions.
17)
32 x − 3 = 4
18)
x=2
x ≈ 0.8856
19)
7 log12 x = 21
20)
53x+1 = 7 2 x−1
2 + log 2 3x = 8
x=
x = 1728
21)
( )
4 2 x = 16
22)
x ≈ −3.7964
(
64
3
)
1 3x+1
2
−2=5
4
x ≈ 1.2691
Find the Inverse of the following functions
23)
f ( x) =
f
25)
−1
2
x−5
3
24)
2
( x ) = 32 ( x + 5 )
f ( x ) = 3x+5
f
26)
f ( x ) = log 25 ( x − 4 )
f −1 ( x ) = 25 x + 4
−1
( x ) = ⎛⎜⎝ x 3+ 1 ⎞⎟⎠ − 5
f ( x ) = 5⋅8x + 2
⎛ x − 2⎞
f −1 ( x ) = log 8 ⎜
⎝ 5 ⎟⎠
f −1 ( x ) = −5 + log 3 x
27)
f ( x) = 3 x + 5 − 1
28)
f ( x ) = 3log12 x + 5
f −1 ( x ) = 2(
x−5 ) 3