1. Topic-
|
| Solving Logarithmic and Exponential Equations |
| |
|
2. Content-
|
Log, Logarithm
Logarithmic Function
Base
Common Log
Natural Log
|
| |
|
3. Goals: Aims/Outcomes-
|
1.State and use the rules of logarithms.
2.Solve exponential equations using logarithms and interpret the real-world
meaning of the results.
3.Solve logarithmic equations using exponentiation and interpret the
real-world meaning of the results.
|
| |
|
|
4. Objectives-
|
1.SWBAT solve for the inverse of a logarithmic function and vice
versa.
2.SWBAT apply log rules to solve problems.
3.SWBAT use log and exponential properties to solve real-world problems. |
| |
|
5. Materials and Aids-
|
| Power Point/Guided Notes/Worksheet |
| |
|
6. Procedures/Methods-
|
|
A. Introduction-
1,000,000 seconds is equivalent to 12 days. How long is one trillion
seconds?
Back thousands of years ago, how do you think mathematicians calculated
with such large numbers? They didn't have a calculator. From patterns
in numbers mathematicians realized exponents (logs) were a helpful
way to calculate with such large numbers. So instead of multiplying
1,000 x 1,000,000, mathematicians could use log base 10^3 and log
10^6 to simplify the numbers. |
| |
|
|
B. Development-
1.Logrithmic functions are inverses of exponential functions.
2.A logarithm is an exponent, and "log" means "the exponent we place
on"
3.A log function is y = log base b (x) and it's inverse is b^y = x.
Show L and e pattern.
4. Common Log Rules - Product Rule, Quotient Rule, and Power Rule.
5. A common log is base 10.
6. A natural log is base e which is equal to 2.718. |
| |
|
|
C. Practice-
1.Solve for y in y = log base 3(81)(I do)
1a. Solve for y in y = log base 2 (16)(we do)
2. Estimate y in y = log base 4(50)
2a. Estimate y in y = log base 2(28)(we do)
3. Solve for y in y = log base 4 (1/16) (I do)
3a. Solve for y in y = log base 4(1/30) (we do)
4. Log(1,000)
4a. Log(100)
5. ln(e^5)
5a. ln (1/4th root of e) |
| |
|
|
D. Independent Practice-
Homework pgs. 376-378, #'s 2-10 even, 14,18,21,22,24,34,45,48,49,54
|
| |
|
|
E. Accommodations (Differentiated Instruction)-
1.Guided notes.
2.Reduced homework.
|
| |
|
|
F. Checking for understanding-
|
|
G. Closure-
|
7. Evaluation-
|
1. Activity sheet 6.4 #1 & #2
2. Homework Quiz |
| |
|
8. Teacher Reflection-
|
Common Errors:
log base (m+n) does not equal log base m + log base n.
log base(m-n) does not equal log base m - log base n
Same of for division and multiplication. Watch this and make sure
students know the rules. |
| |
|