§9.4b
Log Base-Change
Docsity.com
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Log Change Base - Intermediate Algebra - Lecture Slides, Slides of Algebra
Some concept of Intermediate Algebra are Factoring Strategies, Factoring Strategies, Factoring Strategies, Introduction, Inverse_Fcns, Lines_By_Slp-Inter, Log_Change_Base, Multiply Polynomials, Multiply Polynomials. Main points of this lecture are: Log_Change_Base, Logarithm Properties, Positive Numbers, Summary, Log Rules, Typical Log-Confusion, Beware, Algebraically., Converted, Different
Typology: Slides
2012/2013
1 / 19
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Log Change Base - Intermediate Algebra - Lecture Slides and more Slides Algebra in PDF only on Docsity!
§9.4b
Log Base-Change
Review §
Any QUESTIONS About
- §9.4 → Logarithm Properties
Any QUESTIONS About HomeWork
- §9.4 → HW-
9.4 MTH 55
Typical Log-Confusion
- Beware that Logs do NOT behave Algebraically. In General:
log log , log
a a a
M M N N
≠
log ( a MN ) ≠ (log (^) a M )(log (^) a N ),
log ( a M + N ) ≠ log (^) a M + log (^) a N ,
log ( a M − N ) ≠ log (^) a M − log (^) a N.
Change of Base Rule
- Let a , b , and c be positive real numbers
with a ≠ 1 and b ≠ 1.
Then log bx can be converted to a
different base as follows:
log b x =
log a x log a b
=
log x log b
=
ln x ln b (base a ) (base 10) (base e )
Example Evaluate Logs
- Compute log 5 13 by changing to (a) common logarithms (b) natural logarithms
- Soln
b. log 5 13 =
ln ln 5 ≈ 1.
a. log 5 13 =
log log 5 ≈ 1.
Example Evaluate Logs
- Use the change-of-base formula to calculate log 5 12. - Round the answer to four decimal places
- Solution 5
log
log 12
log 5
Check 5 1.5440 = 12.0009 ≈ 12
Example Swamp Fever
Example Swamp Fever
This does NOT = Log
Example Evaluate Logs
- Find the value of each expression withOUT using a calculator a. log 5 3 5 b.^ log1 3 3 c. 7 log1 7^5
Solution a.^ log^5 3 5 =^ log^5
1 3
=
1 3
log 5 5
=
1 3
Example Evaluate Logs
- Solution:
b. log1 3 3 c. 7 log1 7^5
b. log1 3 3 = log (^3) − 1 3 = − log 3 3 = − 1
c. 7 log1 7^5 = 7
log (^7) − 1 5
= 7 −^ log^7
= (^) ( 7 log^7 5 )
− 1
= 5 −^1
=
1 5
Example Curve Fit
- Now find b by Taking the Natural Log of Both Sides of the Eqn
8 = 2 e^3 b 4 = e^3 b ln 4 = 3 b
b =
1 3
ln 4
f (^) ( ) x = 2 e
1 3 ln 4
^
Thus the ae x bx (^) function that will fit the Curve
WhiteBoard Work
Problems From §9.4 Exercise Set
- 70, 74, 76, 78, 80, 82
Log Tables from John Napier, Mirifici logarithmorum canonis descriptio, Edinburgh, 1614.
Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]
Chabot Mathematics
Appendix
r − s ≡^ (^ r − s )( r^ + s )
2 2