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: 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
log4 5=20
Adding logs
When two or more logs with like bases are
added, you multiply the numbers inside the
log.
log (5)+ log (7)
log 35
=1.544
ln(x+3)+ln(x-2)
2
ln(x +x-6)
Subtracting logs
When two or more logs with like bases are
subtracted, you divide the numbers inside
the log.
ln(360)-ln(15)
ln(
360
15
)
ln(24)
=3.178
log(x+7)-log(x)
log( x+7x )
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 5(x+1) is the same as log5(x+1)
1\2ln(25)
ln(√ 25)
ln 5
1.609
Examples
2*5x/4 = 250
2
-Divide both sides by 2
log5125=x/4
-Write as a logarithmic
equation.
4(log5125)=x
-Multiply Both Sides by 4
-Simplify
x=12
Examples
log(3x)=
15
7
15
7
10 =3x
3
x= 46.317
-Re-write as an exponential
equation
-Divide both sides by 3
Examples
ln(x-3)-ln(x)=ln(7)
ln
(x-3)
x
=ln7
x-3=7x
6x=-3
6
x=
-1
2
-Subtract Log's
-Cancel out ln's
-Subtract x from both sides
-Divide both sides by 6
-Simplify
Examples
log2(x+5)+log2 (x+2)=log2 (x+6)
(x+5)(x+2)=(x+6) -In
this situation, because all of
the log bases were the same, they
cancel, leaving just the numbers
2
x +7x+10=x+6
2
x +6x+4=0
-3+√5
-3-√5
inside the logs.
- Multiply
-Simplify
-Use the quadratic formula to find
the answers
Examples
log(x-2)+log(x+5)=2log(3)
2
log(x +3x-10)=log 3
2
x +3x-10=9
-Multiply the logs together
-Cancel the logs and square
3
2
x +3x-19=0
x=3.110
x=-3.110
-Simplify
-Use quadratic formula
You Try!
1.)ln(x-3)+ln(x+4)=3ln(2)
x=-5, x=4
2.)log4(1-x)=1
x= -3
1+√13
2
,
1-√13
2
3.)1\2ln(x+3)-ln(x)=0
x=
4.)logx-(1\2)log(x+4)=1
x=103.85
5.)logx=4
x=10,000
6.)log
x 4(x-5)=-1
x= 21\4
2
7.)4 =96
x=5
8.)4+log3(7x)=10
x=104.143
Newton's Law of
Cooling
T(t)-Tm=(To-Tm)e-Kt
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
(To-Tm)=Initial Temperature of the
T(t)=Temperature of object at time T
Tm=Temperature of surrounding medium object
K=Constant .25387
T=Time
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.
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.
•