Review of Logs and their properties for midchapter test
Name___________________________________
Must show work to get credit. No work= Zero credit.
Date________________
Solve exponential and logarithmic equations. Check the answers for extraneous or no solutions.
1) 4
−3 p
⋅4
p+3
= 16
3) log (−n − 9) = log 2n
2)
1
1
−3x
⋅5 =
25
5
4) log 17 (−3n − 9) = log 17 −n
Solve each equation. Round your answers to the nearest hundredth if needed.
5) log 8 ( x − 4) − log 8 ( x − 3) = log 8 56
6) log 2 9 − log 2 (3x − 5) = 4
7) log (2x 2 − 5) + log 5 = 1
8) log 9 ( x − 6) − log 9 ( x − 3) = log 9 57
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Worksheet by Kuta Software LLC
Condense each expression to a single logarithm.
9) log 4 x − log 4 y − 3 log 4 z
10)
log 7 11
3
+
log 7 5
3
+
log 7 2
3
Expand each logarithm.
11) log 9 (w
u)
4
13) log 8 (ab
)
4 4
12) log 8
14) log
a
3
b
5
()
x
y
3
6
Solve each equation.
15) log 12 x − 1 = 3
16) −3 log 12 b = −6
17) log 12 (9 − 4n) − 8 = −8
18) −8 + log 3 (−2n − 7) = −8
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Worksheet by Kuta Software LLC
Review of Logs and their properties for midchapter test
Name___________________________________
Must show work to get credit. No work= Zero credit.
Date________________
Solve exponential and logarithmic equations. Check the answers for extraneous or no solutions.
1) 4
−3 p
⋅4
p+3
= 16
2)
{}
1
2
3) log (−n − 9) = log 2n
1
1
−3x
⋅5 =
25
5
{ }
−
1
3
4) log 17 (−3n − 9) = log 17 −n
No solution.
{ }
−
9
2
Solve each equation. Round your answers to the nearest hundredth if needed.
5) log 8 ( x − 4) − log 8 ( x − 3) = log 8 56
6) log 2 9 − log 2 (3x − 5) = 4
No solution.
7) log (2x 2 − 5) + log 5 = 1
{1.8542}
8) log 9 ( x − 6) − log 9 ( x − 3) = log 9 57
{1.8708, −1.8708}
No solution.
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Worksheet by Kuta Software LLC
Condense each expression to a single logarithm.
9) log 4 x − log 4 y − 3 log 4 z
log 4
10)
log 7 11
3
x
yz
3
+
3
log 7
log 7 5
3
+
log 7 2
3
110
Expand each logarithm.
11) log 9 (w
u)
4
4 log 9 w +
13) log 8 (ab
12) log 8
log 9 u
)
3
b
5
3 log 8 a − 5 log 8 b
2
4 4
a
14) log
4 log 8 a + 16 log 8 b
()
x
y
3
6
3 log x − 18 log y
Solve each equation.
15) log 12 x − 1 = 3
16) −3 log 12 b = −6
{20736}
17) log 12 (9 − 4n) − 8 = −8
{144}
18) −8 + log 3 (−2n − 7) = −8
{2}
{−4}
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Worksheet by Kuta Software LLC