log inhelp

 | 

  • If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

View
 

Section 3 - Properties of Logarithms

Page history last edited by PBworks 16 years, 4 months ago

Properties Of Logs

 

1.
 
eq=log_a(UV)=log_aU+log_aV
 
When there is a log of a number (that can be writen as the product of two numbers), you can write the log as the sum of the logs of the two factors
 
Ex.
eq=log_56=log_53+log_52 
 
6=(2)(3)
 
2.
eq=log_a(\frac{U}{V})=log_aU-log_aV
 
 When there is a log of a quotient of 2 numbers, you can subtract the log of the denominator from the log of the numerator
 
Ex.
eq=log_5\frac{2}{5}=log_52-log_55 
 
3.
 
eq=log_aU^n=nlog_aU
 
When there is a log of a number to a power you can make the power a coeficient of the log
 
Ex.
eq=log_6x^5=5log_bx
 
 
 
Change of base formula
 
eq=log_ax=\frac{log_bx }{log_ba }  
 
Use to change the base into a common or natural log which can be solved using a calculator
 
 
Ex.
 
eq=log_35=\frac{log_15 }{log_13 }=1.46
 
 
Ex.
 
eq=log_62=\frac{ln2}{ln6}=.39 
 
 
Examples
 Solve using properties of logs
 
Expanding logs:   
ex.eq=log5X^3Y=log5+logX^3+logY
     eq=log5+3logX+logY
     eq=ln=\sqrt{3X-5}/7=ln\sqrt{3X-5}-ln7
     eq=ln(3X-5)^(1/2)-ln7
 
Condensing logs:
ex.eq=1/2logX+3log(x+1)
     eq=logX^(1/2)+log(X+1)^3
     eq=logX^(1/2)(X+3)^3
 
ex. eq=2ln(X+2)-lnX+3ln(X-1)
      eq=ln(X+2)^2-lnX+ln(X-1)^3
      eq=ln(\frac{(X+2)^2(X-1)^3}{X})

Comments (2)

Anonymous said

at 11:59 pm on Dec 20, 2007

no one can top this page

Anonymous said

at 8:33 pm on Jan 8, 2008

The formatting looks good, but take advantage of the fraction and powers options, too! That will definitely help the logs make more sense. 19/20

You don't have permission to comment on this page.

Printable version