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Worksheet 3 Laws of Logarithms
Worksheet 3 Laws of Logarithms
Subject
mathematics
Academic year: 2023/2024
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Unit 9: Laws of Logarithms • Grade 11
Copyright © 2019 Quipper Limited
20
Worksheet III
A. Expand the following logarithmic expressions using the Subtraction Law of
Logarithms. ( 5 points)
1. log $ %
&'(
)&*$
+ ___________________________________________
2. log %
,-. /
0 1 2.
+ ___________________________________________
3. log , 3
4 &(&*()
$ 7 '(
8 ___________________________________________
4. log %
9. : ;
<= 1 >?
+ ___________________________________________
5. log $ 3
,(&*@)(&'A)
(&*()(&'$)
8 ___________________________________________
B. Write the following in a single logarithmic form. ( 5 points)
1. log $ 10 + log $ 𝑥 $ − log $ 5 − log $ 𝑥 − log $ 𝑦 I ___________________________________
2. log(𝑚 + 1 ) − log 9 + log 3 − log(𝑚 $ − 1 ) ___________________________________
3. log , (𝑥 − 2 ) − log , (𝑥 $ + 𝑥 − 6 ) + log , 7 𝑥 ___________________________________
4. log I (𝑥 , + 27 ) − log I (𝑥 − 1 ) − log I (𝑥 $ − 3 𝑥 + 9 ) ___________________________________
5. log , ( 2 𝑥 + 1 ) − log , (𝑥 + 1 ) − 2 ___________________________________
C. Given that log 2 = 𝑤, log 3 = 𝑥, log 5 = 𝑦, and log 7 = 𝑧 write the following logarithmic
expressions in terms of 𝑎, 𝑏, 𝑐, and 𝑑. Write your complete solution to the space
provided. (6 points)
1. log %
,<
A
+
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Worksheet 3 Laws of Logarithms
Subject: mathematics
Was this document helpful?
Unit 9: Laws of Logarithms • Grade 11
Copyright © 2019 Quipper Limited
20
Worksheet III
A. Expand the following logarithmic expressions using the Subtraction Law of
Logarithms. (5 points)
1.
log$
%
&'(
)&*$
+ ___________________________________________
2.
log
%
,-./
012.
+ ___________________________________________
3.
log,
3
4&(&*()
$7'(
8 ___________________________________________
4.
log
%
9.:;
<=1>?
+ ___________________________________________
5.
log$
3
,(&*@)(&'A)
(&*()(&'$)
8 ___________________________________________
B. Write the following in a single logarithmic form. (5 points)
1.
log$10 +log$𝑥$−log$5 − log$𝑥 − log$𝑦I
___________________________________
2.
log
(
𝑚 + 1
)
−log9 + log3 − log(𝑚$− 1)
___________________________________
3.
log,(𝑥 − 2) − log,
(
𝑥$+ 𝑥 − 6
)
+log,7𝑥
___________________________________
4.
logI
(
𝑥,+27
)
−logI(𝑥 − 1) − logI(𝑥$− 3𝑥 + 9)
___________________________________
5.
log,
(
2𝑥 + 1
)
−log,(𝑥 + 1) − 2
___________________________________
C. Given that
log2 = 𝑤
,
log3 = 𝑥
,
log5 = 𝑦
, and
log7 = 𝑧
write the following logarithmic
expressions in terms of
𝑎
,
𝑏
,
𝑐
, and
𝑑
. Write your complete solution to the space
provided. (6 points)
1.
log
%
,<
A
+