Logarithm Properties by Natalie Warnock

Logarithm Properties by Natalie Warnock https://padlet.com/njwarnock/cik7118imfmo and Integration en-us 2017-05-11 14:59:19 UTC 2017-05-23 16:33:18 UTC hello@padlet.com Why log properties? njwarnock https://padlet.com/njwarnock/cik7118imfmo/wish/171287439 It is very easy to make mistakes and not find an answer while integrating if you do not know how to properly use log properties. Therefore, we would like to review log properties before learning integration.]]> 2017-05-11 15:28:02 UTC https://padlet.com/njwarnock/cik7118imfmo/wish/171287439 Part 1 Log Properties Video njwarnock https://padlet.com/njwarnock/cik7118imfmo/wish/171290543 Khan Academy]]> 2017-05-11 15:38:01 UTC https://padlet.com/njwarnock/cik7118imfmo/wish/171290543 Part 2 Log Properties Video njwarnock https://padlet.com/njwarnock/cik7118imfmo/wish/171290770 Khan Academy]]> 2017-05-11 15:38:41 UTC https://padlet.com/njwarnock/cik7118imfmo/wish/171290770 8 Pre-requisite problems FlynnHouse https://padlet.com/njwarnock/cik7118imfmo/wish/171573136 http://tutorial.math.lamar.edu/Classes/CalcI/ExpLogEqns.aspx
Example 1 Solve
7+15e^(1-3x)=10
15e^(1-3x)=3
e^(1-3x)=1/5
ln(e^(1-3x))=ln(1/5)
1-3x=ln(1/5)
-3x=ln(1/5)-1
x=-1/3(ln(1/5)-1)

Example 2 Solve
log(10^{(t^2-t)})=log(100)
t²-t=2
t²-t-2=0
(t-2)(t+1)=0
t=2 t=-1

Example 3 Solve
x-xe^(5x+2)=0
x(1-e^(5x+2))=0
x=0
1-e^(5x+2)=0
e^(5x+2)=1
ln(e^(5x+2))=ln(1)
5x+2=0
x=-2/5

Example 4 Solve
5(x²-4)=(x²-4)e^(7-x)
5(x²-4)-(x²-4)e^(7-x)=0
(x²-4)(5-e^(7-x))=0
x²-4=0
(x+2)(x-2)=0
x=-2 x=2
5-e^(7-x)=0
e^(7-x)=5
ln(e^(7-x))=ln(5)
7-x=ln(5)
x=7-ln(5)]]> 2017-05-12 19:45:26 UTC https://padlet.com/njwarnock/cik7118imfmo/wish/171573136 8 Pre-requisite problems cont. njwarnock https://padlet.com/njwarnock/cik7118imfmo/wish/173238580 Example 5 Solve
4e^(1+3x)-9e^(5-2x)=0
4e^(1+3x)=9e^(5-2x)
(e^(1+3x))/(e^(5-2x))=9/4
e^{(1+3x-(5-2x))}=9/4
e^(5x-4)=9/4
ln(e^(5x-4))=ln(9/4)
5x-4=ln(9/4)
5x=4+ln(9/4)
x=1/5(4+ln(9/4))

Example 6 Solve
3+2ln(x/7+3)=-4
2ln(x/7+3)=-7
ln(x/7+3)=-7/2
e^(ln(x/7+3))=e^(-7/2)
x/7+3=e^(-7/2)
x/7=-3+e^(-7/2)
x=7(-3+e^(-7/2))

Example 7 Solve
2ln(x^(1/2))-ln(1-x)=2
ln((x^(1/2))²)-ln(1-x)=2
ln(x)-ln(1-x)=2
ln(x/(1-x)=2
x/(1-x)=e²
x=e²-(e²)x
x+(e²)x=e²
x(1+e²)=e²
x=e²/(1+e²)

Example 8 Solve
log(x)+log(x-3)=1
log(x(x-3))=1
log(x²-3x)=1
x²-3x=10
x²-3x-10=0
(x-5)(x+2)=0
x=5
x cannot equal -2 because you cannot take the log of a negative number]]> 2017-05-22 19:45:02 UTC https://padlet.com/njwarnock/cik7118imfmo/wish/173238580 2 Calculus Problems njwarnock https://padlet.com/njwarnock/cik7118imfmo/wish/173241997 Example 1
₁∫²2x³/(x⁴+1) dx u=x⁴+1
du=4x³ dx
(1/2) du= 2x³ dx
=(1/2) ₁∫² du/u

= (1/2)ln |u| ]₁²= (1/2)ln |x⁴+1| ]₁^2
=(1/2)ln |2⁴+1| - (1/2)ln |1⁴+1|
= (1/2)ln |17| - (1/2)ln |2|
=(1/2)ln |17/2|

Example 2
₁∫²dx/(20-x) u=20-x
du=-dx
= - ₁∫²du/u
= -ln |u| ]₁²= -ln|20-x| ]₁²= -ln|20-2| - (-ln|20-1|)
= -ln |18| + ln|19|
= ln|19/18|

]]> 2017-05-22 20:08:18 UTC https://padlet.com/njwarnock/cik7118imfmo/wish/173241997 AP Problems njwarnock https://padlet.com/njwarnock/cik7118imfmo/wish/173274984

https://www.slideshare.net/jaflint718/ap-calculus-bc-integration-multiple-choice-practice-solutions

]]> 2017-05-23 01:33:43 UTC https://padlet.com/njwarnock/cik7118imfmo/wish/173274984 Problem Explainations njwarnock https://padlet.com/njwarnock/cik7118imfmo/wish/173369867 Example 1
For this problem we had to use u-sub to find the anti-derivative. But once we found that, we could replace the u and use the given limits and FTC to solve the integral. However, at the end, you must know how to combine logs in order to get the simplest and final answer.

Example 2
We have to use u-sub again in this problem in order to find the anti-derivative of the given integral. After finding it, we are able to replace the u and solve for the answer with the given limits and FTC. We must use logarithm properties in order to combine the logs and get a final answer.]]> 2017-05-23 12:42:39 UTC https://padlet.com/njwarnock/cik7118imfmo/wish/173369867 Kahoot! njwarnock https://padlet.com/njwarnock/cik7118imfmo/wish/173372748 https://play.kahoot.it/#/k/8430381f-89fb-4495-a338-9ea8bc12559e]]> 2017-05-23 12:52:09 UTC https://padlet.com/njwarnock/cik7118imfmo/wish/173372748