LESSON Reteach Properties of Logarithms
[Pages:4]Name
Date
LESSON Reteach 7-4 Properties of Logarithms
Class
Use properties of logarithms to simplify logarithms. The Product Property uses addition instead of multiplication.
Product Property The logarithm of a product can be written as the sum of the logarithm of the numbers.
logb mn logb m logb n where m, n, and b are all positive numbers and b 1
Simplify: log8 4 log8 16 log8 4 16 log8 64 2
The bases must be the same for both logarithms.
Think: 8 to what power is equal to 64, or 8 ? 64.
The Quotient Property uses subtraction instead of division.
Quotient Property
The logarithm of a quotient can be written as the logarithm of the numerator minus the logarithm of the denominator.
logb
_m_ n
logb
m
logb
n
where m, n, and b are all positive numbers and b 1
Simplify: log3 243 log3 9 log3
_2_4_3_ 9
log3
27
3
The bases must be the same for both logarithms.
Think: 3 to what power is equal to 27, or 3 ? 27.
Complete the steps to simplify each expression.
1. log6 54 log6 4 log6 54 4 log6 216
3
2. log2 128 log2 8
log2
_1_2_8_ 8
log2 16
4
3. log9 3 log9 27
log9 3 27 log9 81 2
Copyright ? by Holt, Rinehart and Winston. All rights reserved.
30
Holt Algebra 2
Name
Date
LESSON Reteach 7-4 Properties of Logarithms (continued)
Class
The Power Property uses multiplication instead of exponentiation.
Power Property The logarithm of a power can be written as the product of the exponent and the logarithm of the base.
logb a p p logb a for any real number p where a and b are positive numbers and b 1
Simplify: log4 64 5 5 log4 64 5 3 15
"Bring down" the exponent to multiply.
Think: 4 to what power is equal to 64, or 4 ? 64.
Logarithms and exponents undo each other when their bases are the same.
Inverse Properties
The logarithm of bx to the base b is equal b raised to the logarithm of x to the base b
to x.
logb b x x
is equal to x.
b logb x x
FF
The logarithm undoes the exponent when
the bases are the same.
FF
The exponent undoes the logarithm when
the bases are the same.
Simplify: log7 7 4x 4x
Simplify: 3 log3 64 64
The base of the log is 7 and the base of the exponent is 7.
The base of the exponent is 3 and the base of the log is 3.
Simplify each expression. 4. log5 125 2
2 log5 125
2 3 6
7. log6 6 5y
5y
5. log2 16 4 4 log2 16
4 4 16
8. 4 log4 75
75
6. log9 81 3
3 log9 81
3 2 6
9. 2 log2 3x
3x
Copyright ? by Holt, Rinehart and Winston. All rights reserved.
31
Holt Algebra 2
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Copyright ? by Holt, Rinehart and Winston. All rights reserved.
73
Holt Algebra 2
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Copyright ? by Holt, Rinehart and Winston. All rights reserved.
74
Holt Algebra 2
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