(4) Show and explain why the following equation is TRUE or FALSE.
e -ln c = -c
Our group believes this equation is FALSE...
because
as an example, when we sub in the number "2" in for "c"
e -ln c = -c
e -ln(2) = -(2)
0.5 = -2
As you can see... both sides of the equation don't equal each other...
Therefore the equation is FALSE...
In order to make the equation become TRUE, our group came up with two methods.
METHOD 1:
ORIGINAL EQUATION: e-ln c = -c
We changed "-c" to " 1/c " (both negative reciprocals of each other) and we sub in the number "2" in for "c" in order to make both sides equal.
e -ln c = 1/c
e -ln (2) = 1/(2)
0.5=0.5 =] they equal
METHOD 2:
ORIGINAL EQUATION: e -ln c = -c
In this case, we took the negative (-) out of both "ln c" and "c" and we sub in the number "2" in for "c" in order to make both sides equal.
e ln c = c
e ln (2) = (2)
2=2 =] they equal
So yeah... that's what our group came up with! If anyone has any comments regarding any mistakes we've made, feel free to comment! ; )
12 comments:
Yay, you gys got the answer right!THanks for stating a two methods where the equation would be right!
THe first method where e^-Ln(c) = 1/c is right because when we try to get rid of the exponent
-Lnc ,it would look like this:
1.) -Ln(c)[Ln(e)]=1/c
2.) we know that "Ln(e)"=1
-Ln(c)[1]=1/c
3.) we know that "-Ln(c)"=c^-1
c^-1=1/c
4.) we know that "c^-1"= 1/c
because its like saying
: x^-y=1/x^y
1/c=1/c
Method 2 also work. but u gys got an idea why it work, so yeah. i need to go sleep now. My brain is hurting.I still need to go to work to tmmrw.
Good job Group 4!
wow, good work guys. you found 2 methods to make the equation right. i think you got the answer correct and by looking at your explanations, i feel confident agreeing with you.
be happy, you did great.
I agree that it is false.
e^ -ln(c) does not equal c
A logarithm is an exponent.
It can be written as e^ ln(c)^(1/2), and that does not equal c.
This is a common error people make.
Good stuff.
I agree that the equation is false. Its obvious that when you plug 2 into the equation, the two sides don't equal. Good job on coming up with two methods on how to make the equation true. Awesome job guys.
I also agree that this equation is false. And it appears that both your methods for making it true work. The only thing I might add is that maybe instead of just subbing in values to prove it, you could also show how it would look if you used variables. I'm not sure if that makes sense exactly, but I don't know how to say it.
I agree that the equation is false. Not only did you guys show why it is false, you also came up with two methods that work. Your explanations are thorough. Plugging values in the variables make it easy to understand why the equation is false. nicely done i say, nicely done =)
I agree with your answer that the equation is false because you provided an example that showed that. I think your group did a very good job at finding two possible methods for correcting the false equation to make it so that it is true.
Great job guys, Two methods on how to correct the equation! Both were very easy to understand. I liked how you use examples for all the methods. But is there another way, like using logarithmic rules instead of plugging in numbers? Just curious.
Your explanation was very easy to understand and helped me. Your group did a great job. I liked that you had two methods of explaining. That way people have a way of choosing which way they like using. I also agree with Crystal's comment, is there another way to figure out this problem besides substituting in numbers?
My opinion could be bad because I've seen all the other comments already. It might make my decision biased. However, based on this group's explanations and some of the comments I've read, I have to say I also believe this equation is false. The two methods you came up with for a solution are good.
Whops, I just noticed an error in my comment. It can be written as e^ln(1/c), not the thing I wrote above. Annd that does not equal c. Sorry!
Great use of colours on your post. Everything is very understandable an I agree with your answer. You gave c an value and just tried solving it which gave you different values on each side of the equal, making it false. The fact that you guys gave TWO methods of making the original equation true was great. Both made the equation true, and both are right. Good job!
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