1 / 17

You may need to close viewing mode to open the window that the link opens up

You may need to close viewing mode to open the window that the link opens up. What is a Log Equation:. ~ A log equation is a different way of writing an exponential equation. For example: 4 20 =5 can be written as log 4 5=20. The Way this works is: . You write log

tracey
Download Presentation

You may need to close viewing mode to open the window that the link opens up

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. You may need to close viewing mode to open the window that the link opens up

  2. What is a Log Equation: ~ A log equation is a different way of writing an exponential equation. For example: 420=5 can be written as log45=20 The Way this works is: • You write log • You put the base # is subscript • Then write the # that the original equation is equal to • Put in the = sign • Write the exponent log 5 20 = 4

  3. Adding logs When two or more logs with like bases are added, you multiply the numbers inside the log. ln(x+3)+ln(x-2) log (5)+ log (7) log 35 ln(x +x-6) 2 =1.544

  4. Subtracting logs When two or more logs with like bases are subtracted, you divide the numbers inside the log. log(x+7)-log(x) ln(360)-ln(15) ln( ) 360 15 log( ) x+7 x ln(24) =3.178

  5. Numbers in front of logs Numbers in front of logs are the same thing as having the number inside the log to a power. so... 2log (x+1) is the same as log (x+1) 5 5 √ ln( 25) ln 5 1.609 1\2ln(25)

  6. Examples 2*5x/4 = 250 2 -Divide both sides by 2 -Write as a logarithmic equation. -Multiply Both Sides by 4 -Simplify log5125=x/4 4(log5125)=x x=12

  7. Examples 15 15 log(3x)= 7 7 -Re-write as an exponential equation 10 =3x 3 -Divide both sides by 3 x= 46.317

  8. Examples ln(x-3)-ln(x)=ln(7) (x-3) ln =ln7 -Subtract Log's x x-3=7x -Cancel out ln's -Subtract x from both sides 6x=-3 6 -Divide both sides by 6 -1 x= -Simplify 2

  9. Examples log (x+5)+log (x+2)=log (x+6) 2 2 2 -In this situation, because all of the log bases were the same, they cancel, leaving just the numbers inside the logs. (x+5)(x+2)=(x+6) x +7x+10=x+6 2 - Multiply x +6x+4=0 2 -Simplify √ -3+ 5 -3- 5 √ -Use the quadratic formula to find the answers

  10. Examples log(x-2)+log(x+5)=2log(3) 2 log(x +3x-10)=log 3 -Multiply the logs together 2 x +3x-10=9 -Cancel the logs and square 3 2 x +3x-19=0 -Simplify x=3.110 -Use quadratic formula x=-3.110

  11. You Try! x=-5, x=4 x= -3 x= , x=103.85 x=10,000 x= 21\4 x=5 x=104.143 1.)ln(x-3)+ln(x+4)=3ln(2) 2.)log (1-x)=1 3.)1\2ln(x+3)-ln(x)=0 4.)logx-(1\2)log(x+4)=1 5.)logx=4 6.)log (x-5)=-1 7.)4 =96 8.)4+log (7x)=10 4 √ 1- 13 √ 1+ 13 2 2 4 x 2 3

  12. Newton's Law of Cooling T(t)-Tm=(To-Tm)e-Kt

  13. Newton's Law of Cooling What Its Used For • Newton’s Law of Cooling is used to measure the amount of heat lost over a period of time. This equation is often used in Occupations such as Crime scene investigation, where investigators examine bodies to see how long the person has been dead for. • T(t)-Tm=(To-Tm)e-Kt T(t)=Temperature of object at time T Tm=Temperature of surrounding medium (To-Tm)=Initial Temperature of the object K=Constant .25387 T=Time

  14. Example • Lets say we (hypothetically) find Chris Kryshak “Accidentally” killed by someone. On the body we find a post-it note left by the killer (definitely not Eric Weber) That says the temperature on death was 37 degrees Celsius. Investigators determine that the current temperature of the body is 30degrees Celsius, and today is a warm day at 29 degrees Celsius. Using T(t)-Tm=(To-Tm)e-Kt we can determine how long Chris has been dead.

  15. Figuring Out What Time the Killer (Cough*Eric*Cough) killed Chris • T(t)-Tm=(To-Tm)e-Kt Original Equation • 30-29=(37)e.25387(T) Subtract 29 from 30 • 1=(37)e.25387(t) divide 1 by 37 • .02702703=e.25387(t) convert to Ln • Ln.02702703=.25387t find Ln.02702703 • -3.610917803=.25387t Divide -3.610917803 by .25387 • T= -14.22349156* So, We have determined that Chris was killed by someone (who isn’t Eric) 14.22349156 hours ago. *This Number is a negative because it is looking at the time that has passed.

More Related