Review Sheet: Exponential and Logorithmic Functions Date ...
Math 120
ID: 1
Name___________________________________
Review Sheet: Exponential and Logorithmic Functions Date________________ Period____
Expand each logarithm.
( )u 2 3
1) log v
2) log 6 (u ) 4v4
3) log 5 3 8 7 11
4) log 4 (u ) 6v5
( )x 4 3
5) log 3 y
Condense each expression to a single logarithm. 6) ln 5 + ln 7 + 2 ln 6
7) 4 log 2 6 + 3 log 2 7
8) log 8 x + log 8 y + 6 log 8 z
9) 18 log 9 x - 6 log 9 y
10)
4 log 8
7 +
log 8 3
6
Rewrite each equation in exponential form. 11) log 2 32 = 5
1 13) log 19 361 = -2
1
15)
log 1
= 2 81
9
12) log 5 125 = 3 14) log 6 216 = 3
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Worksheet by Kuta Software LLC
Rewrite each equation in logarithmic form. 16) 42 = 16 18) m3 = n 20) a-7 = b Find the inverse of each function. 21) y = log 6 x2
23) y = log 5 (-3x)
17) x-4 = y 19) 12 x = y
22) y = -10 log 4 x 24) y = log 5 x3
25) y = 3 log 5 x
4 x 26) y =
4
e x 27) y =
3
4 x 28) y =
2
29) y = 3 x + 8
30) y = 3 x - 10
Solve each equation.
31) log 11 (-2x - 6) = log 11 (x + 9) 33) log (2k - 4) = log k 35) log 9 1 = log 9 (1 - 4x) 37) log 6 (x - 4) + log 6 4 = log 6 45
32) log 18 (5a - 1) = log 18 4a 34) log 13 ( p + 5) = log 13 (2 p - 4) 36) log 5 (x + 6) - log 5 2 = 2 38) log 5 (x - 10) - log 5 3 = 2
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-2-
Worksheet by Kuta Software LLC
39) log 4 -x + log 4 8 = 5
Sketch the graph of each function.
41) y = log 2 (x - 2) - 5
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
43) y = log 4 (x + 2) - 5
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
45) y = log 5 (x - 1) - 2
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
40) log 3 5x - log 3 7 = 1
42) y = log 3 (x + 2) - 5
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
44) y = log 3 (x - 3) + 5
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
46) y = log 4 (x - 1) - 5
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
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-3-
Worksheet by Kuta Software LLC
47) y = log 5 (x - 1) + 2
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
49) y = log 6 (x + 6) + 5
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
( )1 x
51) y = 5 2
20 18 16 14 12 10 8 6 4 2
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
48) y = log 4 (x + 5)
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
50) y = log 5 (x + 1) + 4
y 8
6
4
2
-8 -6 -4 -2 -2 -4 -6 -8
2 4 6 8x
52) y = -2 2 x
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20
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-4-
Worksheet by Kuta Software LLC
53) y = -3 2 x
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20
( )1 x
55) y = 4 2
20 18 16 14 12 10 8 6 4 2 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
( )1 x
54) y = 3 2
20 18 16 14 12 10 8 6 4 2
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
( )1 x
56) y = -4 2
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20
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-5-
Worksheet by Kuta Software LLC
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