Mrs. Snipes...I could not find where to post the information about Lesson 8-4 so I'm just going to post my comment here!
Lesson 8-4: Properties of Logarithms
Objectives: To know and understand the properties of logarithms and to use the properties of logarithms.
Properties: Product Property: log base b MN= log base b M+ log base b N For example: log base b X^3 + log base b Y= log base b X^3Y
Quotient Property: log base b M/N= log base b M- log base b N For example: log base 2 8- log base 2 16= log base 2 8/16 which reduces to 1/2
Power Property: log base b M^X= X log base b M For example: log base 2 X^3= 3 log base 2 X
On the first side of the equal signs in all the properties above is called the condensed form of the property. The expanded form of a property is when you add, subtract, or have an exponent in the beginning equation.
Another important fact to remember is that if the bases (b) do not match, you have to solve the logs separately or they will have no solution.
Simplifying Logs -Write log base 3 10 as a sum: log base 3 2 + log base 3 5 -Write log base 3 10 as a difference: log base 3 20/2= log base 3 20- log base 3 2 -Write 3 log 2 + log 3 as a single log: log 2^3 = log 3= log 2^3times 3 -Write 2 log base 3 7- log base 3 6 as a single log: log base 3 7^2- log base 3 6=log base 3 46
Jon, Your 8.3 summary is good, but could you tell us the formula used to solve for pH and also the formula used to solve for the Hydrogen ion concentration of a substance?
Objectives 1.)Write and evaluate log expressions 2.)Graph log Functions
*The Logarithmic Function is the Inverse of the Exponential Function.*
If y=b^x, then its inverse is x=b^y Since the equation can not be solve for y, change it to logritmic form which is y=log base b X (log base b X)=(b^y=x) Another way of writing it is, log base b N=P and b^p=N ~b=base ~N=number ~P=power *Restrictions* b>0 and b can not equal 1 N>0 because the log of zero or a negative number is undefined. The x-intercept is (1,0) The asymptote is the y-axis *How to change from Exponential Form to Log Form* -Log Form:log base b N=P -Exponential Form:b^p=N *Examples* log base_2_8=3 - 2^3=8 log base_10_1000=3 - 10^3=1000 log base_4_16=2 - 4^2=16 *Evaluate* log base_4_16=2 log base_10_100=2 log base_3_81=4 ~Common and Natural Logs~ A common logarithim is a log that uses 10 as its base Log2=.301 Examples: Log50=1.7 Log100=10 -Natural logs which are base e and common logs which are base10. Examples: LN_e_3=1.10 LN 1=0 LN_e_=1 LN 0= can not equal 0 Some common logs are Log100,Log50,Log26.2 and Log1/4 Logs are also uses to measure acidity. *Acidity increases as the concentration of hydrogen ions in a substance increases.* The formula we use is pH=-log[H+] -where H+ is the concentration of hydrogen ions *If given pH use 10^-pH=H+ and solve for H+. *If given H+ use -log_10_H+=pH and solve for pH.
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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Mrs. Snipes...I could not find where to post the information about Lesson 8-4 so I'm just going to post my comment here!
Lesson 8-4: Properties of Logarithms
Objectives: To know and understand the properties of logarithms and to use the properties of logarithms.
Properties:
Product Property:
log base b MN= log base b M+ log base b N
For example: log base b X^3 + log base b Y= log base b X^3Y
Quotient Property:
log base b M/N= log base b M- log base b N
For example: log base 2 8- log base 2 16= log base 2 8/16 which reduces to 1/2
Power Property: log base b M^X= X log base b M
For example: log base 2 X^3= 3 log base 2 X
On the first side of the equal signs in all the properties above is called the condensed form of the property. The expanded form of a property is when you add, subtract, or have an exponent in the beginning equation.
Another important fact to remember is that if the bases (b) do not match, you have to solve the logs separately or they will have no solution.
Simplifying Logs
-Write log base 3 10 as a sum: log base 3 2 + log base 3 5
-Write log base 3 10 as a difference:
log base 3 20/2= log base 3 20- log base 3 2
-Write 3 log 2 + log 3 as a single log: log 2^3 = log 3= log 2^3times 3
-Write 2 log base 3 7- log base 3 6 as a single log: log base 3 7^2- log base 3 6=log base 3 46
Expanding Logs
log base 2 (X/Y)= log base 2 X- log base 2 Y
log 4 X^3= log base 4 + 3 log base x
log (Y/3)^4= 4 log Y- 4 log 3
That's all folks!
8.3 Logarithmic Functions as Inverses
-Objectives
1. Write and evaluate log expressions
2. Graph Log Functions
If y = b^x then its inverse is x=b^y
this means that LOG_b_X equals b^y=x
logbN = P
and b^p=n
B represents the base
N is the number
P is the power
b>0 and cannot equal 1
n>0
Examples of how to change from log form to exponential form...
Log_2_8 = 3 = 2^3 = 8
Common logarithms use 10 as their base
common logs are log100 log50 log26.2 log(1/4)
Logs are oftem used to measure various things such as acidity.
Homework for this lesson was assigned tuesday and is P 442 6-34 41-49 53-61
Hi Kristy,
Your summary is good. I didn't do a post for 8.4 until late this afternoon. That's why you couldn't find it. Thanks
Mrs. S
Jon,
Your 8.3 summary is good, but could you tell us the formula used to solve for pH and also the formula used to solve for the Hydrogen ion concentration of a substance?
Wishing for snow....
Mrs. S
Lesson 8-3
Logritmic Functions as Inverse
Objectives
1.)Write and evaluate log expressions
2.)Graph log Functions
*The Logarithmic Function is the Inverse of the Exponential Function.*
If y=b^x, then its inverse is x=b^y
Since the equation can not be solve for y, change it to logritmic form which is
y=log base b X
(log base b X)=(b^y=x)
Another way of writing it is,
log base b N=P and b^p=N
~b=base
~N=number
~P=power
*Restrictions*
b>0 and b can not equal 1
N>0 because the log of zero or a negative number is undefined.
The x-intercept is (1,0)
The asymptote is the y-axis
*How to change from Exponential Form to Log Form*
-Log Form:log base b N=P
-Exponential Form:b^p=N
*Examples*
log base_2_8=3 - 2^3=8
log base_10_1000=3 - 10^3=1000
log base_4_16=2 - 4^2=16
*Evaluate*
log base_4_16=2
log base_10_100=2
log base_3_81=4
~Common and Natural Logs~
A common logarithim is a log that uses 10 as its base
Log2=.301
Examples:
Log50=1.7
Log100=10
-Natural logs which are base e and common logs which are base10.
Examples:
LN_e_3=1.10
LN 1=0
LN_e_=1
LN 0= can not equal 0
Some common logs are Log100,Log50,Log26.2 and Log1/4
Logs are also uses to measure acidity.
*Acidity increases as the concentration of hydrogen ions in a substance increases.*
The formula we use is
pH=-log[H+]
-where H+ is the concentration of hydrogen ions
*If given pH use 10^-pH=H+ and solve for H+.
*If given H+ use -log_10_H+=pH and solve for pH.
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