SE MRC College Algebra Content Review
Properties of Logarithms
Section 4.3
(Don’t forget to look for the logarithmic properties handout.)
3. Use properties of logarithms to expand the
logarithmic expression as much as possible.
Evaluate logarithmic expressions without using a
calculator if possible.
13
log13 ( )
𝑦
Learning Objectives:
1.
2.
3.
4.
5.
6.
Use the product rule.
Use quotient rule.
Use the power rule.
Expand logarithmic expressions.
Condense logarithmic expressions.
Use the change-of-base property.
1. Use properties of logarithms to expand the
logarithmic expression as much as possible. When
possible, evaluate logarithmic expressions without
using a calculator.
log 8 (11 ∙ 13)
2. Use properties of logarithms to expand the
logarithmic expression as much as possible. When
possible, evaluate logarithmic expressions without
using a calculator.
4. Use properties of logarithms to expand the
logarithmic expression as much as possible.
Evaluate logarithmic expressions without using a
calculator if possible.
𝑒2
ln ( )
14
log(100𝑥)
Tarrant County College District
Section 4.3
Revised 6/04/2015
5. Use properties of logarithms to expand the
logarithmic expression as much as possible. Where
possible, evaluate logarithmic expressions without
using a calculator.
8. Use properties of logarithms to expand the
logarithmic expression as much as possible.
Evaluate logarithmic expressions without using a
calculator if possible.
log 𝑏 (𝑥 3 )
6. Use properties of logarithms to expand the
logarithmic expression as much as possible.
Evaluate logarithmic expressions without using a
calculator if possible.
𝑥2𝑦
log 𝑏 ( 6 )
𝑧
9. Use properties of logarithms to expand the
logarithmic expression as much as possible.
log 𝑑
13
√𝑎𝑏 5
𝑐2
ln √𝑥
7. Use properties of logarithms to expand the
logarithmic expression as much as possible.
Evaluate logarithmic expressions without using a
calculator if possible.
10. Use properties of logarithms to condense the
logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.Where
possible, evaluate logarithmic expressions.
log 𝑏 (𝑥 7 𝑧)
Tarrant County College District
log 125 + log 8
Section 4.3
Revised 6/04/2015
11. Use properties of logarithms to condense the
logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.Where
possible, evaluate logarithmic expressions.
14. Use properties of logarithms to condense the
logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.Where
possible, evaluate logarithmic expressions.
1
ln 𝑦 + ln 𝑧
3
ln(𝑥) + ln 20
12. Use properties of logarithms to condense the
logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.Where
possible, evaluate logarithmic expressions.
15. Use properties of logarithms to condense the
logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.Where
possible, evaluate logarithmic expressions.
2 log 𝑏 𝑥 + 7 log 𝑏 𝑧
log 4 24 − log 4 6
13. Use properties of logarithms to condense the
logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.Where
possible, evaluate logarithmic expressions.
16. Use properties of logarithms to condense the
logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.Where
possible, evaluate logarithmic expressions.
1
7 ln 𝑥 − ln 𝑦
4
log(5𝑥 + 1) − log(𝑥)
Tarrant County College District
Section 4.3
Revised 6/04/2015
17. Use properties of logarithms to condense the
logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.Where
possible, evaluate logarithmic expressions.
20. Use common logarithms or natural logarithms and
a calculator to evaluate the expressions. (Round to
four decimal places as needed)
log 0.3 28.6
2 ln 𝑥 + 5 ln 𝑦 − 4 ln 𝑧
18. Use common logarithms or natural logarithms and
a calculator to evaluate the expressions. (Round to
four decimal places as needed)
log16 12
Answer Key:
1.
2.
log 8 11 + log 8 13
2 + log 𝑥
3.
1 − log13 𝑦
4.
5.
2 − ln 14
3 log 𝑏 𝑥
1
ln 𝑥
13
7 log 𝑏 𝑥 + log 𝑏 𝑧
2 log 𝑏 𝑥 + log 𝑏 𝑦 − 6 log 𝑏 𝑧
1
log 𝑎 + 5 log 𝑑 𝑏 − 2 log 𝑑 𝑐
2 𝑑
3
ln(20𝑥)
1
5𝑥 + 1
log
𝑥
ln(𝑧 3√𝑦)
log 𝑏 (𝑥 2 𝑧 7 )
𝑥7
ln 4
√𝑦
𝑥2𝑦5
ln ( 4 )
𝑧
0.8962
1.6987
−2.7853
6.
7.
8.
19. Use common logarithms or natural logarithms and
a calculator to evaluate the expressions. (Round to
four decimal places as needed)
log14 88.5
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Tarrant County College District
Section 4.3
Revised 6/04/2015