Chapter 6.5
6.5 Properties of Logarithms
Warm ups
Determine the value of n in the expression.
1.
2.
3.
4.
5.
6.
Solve the equation. Write your answer in simplest form.
1. 2 (x − 3)2 = 8
2. 6x2 − 7x − 20 = 0
3. x2 − 4x − 8 = 0
4. 6x − 3x2 = 15
5. x2 = 6x − 9
6.
(3x + 1)2 = −5
Chapter 6.5
6.5 Properties of Logarithms
How can you use properties of exponents to
derive properties of logarithms?
Evaluate.
Evaluate.
1. log416 + log44 = __________
log4(16•4) = ____________
log100 + log100 = __________
log (100•100) = ___________
2. 3log28 = _____________
log283 = _____________
3log525 = _____________
log5253 = ____________
Generalization
Product Property:
Power Property:
Quotient Property:
3. log264 - log232 = __________
log2(64/32) = ______________
ln e12 - ln e4 = ____________
ln (e12/e4 ) = _____________
Chapter 6.5
For 1 and 2, evaluate.
1. log 2 + log 108
6
2. log 5 + log 45
6
15
15
For 3 and 4, solve.
3. 1/2 log225 = x
4. log540 - log58 = x
Use log2 3 ≈ 1.585 and log27 ≈ 2.807 to evaluate each logarithm.
a. log2
b. log2 21
c. log2 49
Chapter 6.5
Use log6 5 0.898 and log6 8 1.161 to evaluate the logarithm.
5. log6
6. log6 40
7. log6 64
8. log6 125
Expand the logarithmic expression.
9. log6 3x4
10. ln
Condense the logarithmic expression.
11. log x − log 9
c. Expand.
ln
12. ln 4 + 3 ln 3 − ln 12
d. Condense.
log 9 + 3 log 2 − log 3.
Chapter 6.5
Evaluate log3 8 using common logarithms.
Evaluate log6 24 using natural logarithms.
Use the change-of-base formula to evaluate the logarithm.
13. log5 8
14. log8 14
15. log26 9
16. log12 30
Chapter 6.5
Use log32 ≈ .6310 and log37 ≈ 1.7712 to approximate the
value of each expression.
1. log349
2. log318
3. log354
4. log3