AP Calculus AB (2006-07)

September 22, 2006

GROUP #2 : Ashlynn, Charlotte and Anh.

Is the following equation TRUE or FALSE?
Ln(A+B) = (LnA)(LnB)

Our answer is FALSE. We proved our answer by using an example.

ex: Let A=2 and B=3

Ln(2+3) = (Ln2)(Ln3)
Ln(5) = (Ln2)(Ln3)
(1.6094) = (.6931)(1.0986)
(1.6094) = (.7615)

Both sides of the equation do not equal each other, therefore the original equation is false.

A common error for this particular equation is that people may think they can go from Ln(A)Ln(B) to Ln(AB), but you can't because the logarithm laws do not allow you to do so.

So the correct answer would be:
Ln(AB) = Ln(A) + Ln(B)

11 comments:

christian said...: I think I agree with your answer. We should remember that LOGARITHMS ARE EXPONENTS right?? That is the reason why the laws of exponents apply to logs. This group has stated that ln(A)ln(B) is not equal ln(AB). I think I can live with that XD.; 9/22/2006 10:01 PM
♫ Jann ♫ said...: I agree with your answer. Since the values dont equal each other, its false. If you look at the pattern of ln(A) + ln(B), the answer is ln(A+B) which is true. The formula you came up with is very reasonable.; 9/22/2006 11:10 PM
lindsay said...: i also agree with your answer. since you provided us with an example, your answer looks right. you also included how we can make mistakes with the logarithm laws.

good job guys.; 9/22/2006 11:47 PM
charlotte said...: Im so proud at my group, we realy used the time in class to finish answering our question. As u can see on the blog,the Ln(A+B)=(LnA)(LnB) is False and the correct formula is :
Ln(AB)=Ln(A)+Ln(B)
its right because if u let:
A=2 and B=3
1.) ln(2*3)=ln(2)+ln(3)
2.) ln(6)=(.6931)+(1.0986)
3.) 1.7918=1.7918; 9/23/2006 12:53 AM
char__lene said...: i completely agree with your answer. I remember Mr.K saying in previous classes that you can't do log(A+B)=(logA)(logB). good job on coming up with the right method to make it true.; 9/23/2006 9:29 AM
Anonymous said...: i think your answer is right too, b/c if both sides of the equation don't equal, then the equation is FALSE. In the true equation, Ln(AB) = Ln(A) + Ln(B, when i plug in say "4" for "A" and "5" for "B" both sides of the equation equal 2.9957! Therfore u guys are right!!! :); 9/23/2006 11:26 AM
Suzanne said...: I agree with you guys as well. I guess it makes sense that someone would make that mistake with the equation. They simply switched which side of the equation was added and which was multiplied. So I'd say you got the right idea as to what the equation is supposed to be. good job :); 9/23/2006 1:39 PM
Anonymous said...: I also agree with your answer. Your explanation is simple. Nothing fancy shmancy (if that's even a word) and straightforward. I've made that "common error" in the past, and it haunts me to this day, lol. I've definitely learned my lesson... good job guys =); 9/23/2006 4:41 PM
crystal said...: I agree with your answer; that it's false. Some people might have thought that addition and multiplicaiton have a connection, therefore would have thought this was true. Because sometimes in math adding and multiplying are connected. I don't know if this makes any sense to anyone. Anyways your group explained this well with an example. Simple and sweet.; 9/23/2006 9:27 PM
Manny said...: The equation is false. I agree with your group, and the explanation leaves me without words. But I'll do so anyway =D. A logarithm is an exponent. When adding exponents you're multiplying the powers.; 9/24/2006 11:41 AM
Mr. Ly said...: I agree with this groups answers, they gave an example to how it's false and you can SEE that it's false. Good job on stating the common error and providing the correct answer that I also agree with. Overall, very understandable.; 9/24/2006 10:00 PM