Vocabulary Terms: 1. Exponential Equation- An equation of the form b^cx=a, where the exponent includes a variable.
2. Change of Base Formula- log base b of M= Log base c of M divided by log base c of b. Where M, b, and c are positive numbers and b is not equal to one and c is not equal to one.
3. Logarithmic Equation- An equation that includes a logarithmic expression. Example: 2=3^4x
How to Solve. 1. If there is a prequal simplify it. 2. Change to log equation log 2=log3^4x 3. Use power rule (log2)=(4x)(log3) ------ --------- (4log3) 4log3 4. Solve for x x= .1577
To evaluate logs with bases other than ten and e without a calculator. example: e=2^x Steps: 1. Write natural log in front of both sides. Natural log is ln lne=ln2^x 2. Solve for x lne =(x)(ln2) ----- ------- ln2 ln2 Answer= 1.4427
To use the Change of Base Formula or the C. O. B. **Remember that the Number goes in the numerator and the base goes on the bottom** Steps: 1. Use C of b to write a common log. 2. Take base and raise to answer, set equal to x. log base b of N= logN ---- logb
Example: log base 3 of 15= log base 2 of 15 ---------------- log3 = 2.4650 log base 2 of x= 2^2.4650=x=log base2 5.5213
Lesson 8.5 Objectives: solve exponential equations and logarithmic equations
Vocabulary exponential equation-equation in the form of b raised to cx =a, exponent includes a variable
change of base formula- log base b of m= log base c of m divided by log base=se c of b, m, c, and b are positive numbers and b and c are not equal to one. log N / log B
logarithmic equation- equation that includes a logarithmic expression ex. 5 raised to 2x equals 16
to solve an exponential equation: prequal: simplify 1. write log on both sides or ln 2. use power rule 3. solve for x Ex.2=3 raised to (4x) log2=log3 raised to (4x) divide log 2 by 4log3 (log2)/(4log3)=x
To solve a logarithmic equation: 1. simplify until you have log base b of N =P 2.change to b raised to p =N and solve
I teach AP Calculus, Pre AP Precalculus, and Advanced Algebra/Trigonometry at Muscle Shoals High School. In my spare time, I enjoy spending time with my family and granddaughters. My husband and I like to travel and visited Germany and France last summer. I also enjoy reading, art and music.
Last spring, I read The Other Boleyn Girl by Philippa Gregory. I am currently reading the Constant Princess (by the same author).
I love "anything about England".
"SUGGESTED READING LIST" The Mathematical Traveler. It is a great book that combines history and interesting facts about famous mathematicians. See me if you want to "check it out".
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Lesson 8.5
Exponential & Logarithmic Equations
Objectives:
1. Solve Exponential Equations.
2. Solve Logarithmic Equations.
Vocabulary Terms:
1. Exponential Equation- An equation of the form b^cx=a, where the exponent includes a variable.
2. Change of Base Formula- log base b of M= Log base c of M divided by log base c of b. Where M, b, and c are positive numbers and b is not equal to one and c is not equal to one.
3. Logarithmic Equation- An equation that includes a logarithmic expression.
Example: 2=3^4x
How to Solve.
1. If there is a prequal simplify it.
2. Change to log equation
log 2=log3^4x
3. Use power rule
(log2)=(4x)(log3)
------ ---------
(4log3) 4log3
4. Solve for x
x= .1577
To evaluate logs with bases other than ten and e without a calculator.
example:
e=2^x
Steps:
1. Write natural log in front of both sides. Natural log is ln
lne=ln2^x
2. Solve for x
lne =(x)(ln2)
----- -------
ln2 ln2
Answer= 1.4427
To use the Change of Base Formula or the C. O. B.
**Remember that the Number goes in the numerator and the base goes on the bottom**
Steps:
1. Use C of b to write a common log.
2. Take base and raise to answer, set equal to x.
log base b of N= logN
----
logb
Example:
log base 3 of 15= log base 2 of 15
----------------
log3
= 2.4650
log base 2 of x= 2^2.4650=x=log base2 5.5213
Lesson 8.5
Objectives: solve exponential equations and logarithmic equations
Vocabulary
exponential equation-equation in the form of b raised to cx =a, exponent includes a variable
change of base formula- log base b of m= log base c of m divided by log base=se c of b, m, c, and b are positive numbers and b and c are not equal to one.
log N / log B
logarithmic equation- equation that includes a logarithmic expression ex. 5 raised to 2x equals 16
to solve an exponential equation:
prequal: simplify
1. write log on both sides or ln
2. use power rule
3. solve for x
Ex.2=3 raised to (4x)
log2=log3 raised to (4x)
divide log 2 by 4log3
(log2)/(4log3)=x
To solve a logarithmic equation:
1. simplify until you have log base b of N =P
2.change to b raised to p =N and solve
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