How is this equality possible? What did the professor do to reach it?

  • Thread starter Thread starter tahlaskerssen
  • Start date Start date
  • Tags Tags
    Professor
AI Thread Summary
The discussion revolves around understanding how to manipulate mathematical expressions involving logarithms and summations. A participant seeks clarification on how to combine terms in the expression A. ln Q - A. ln w, where A represents a common summation. The explanation highlights that since both terms share the same summation range, they can be combined into a single series using one sigma notation. Additionally, it emphasizes the logarithmic identity ln Q - ln w = ln (Q/w) and its simplification. The participant expresses relief and newfound understanding after the clarification, indicating a positive learning experience.
tahlaskerssen
Messages
10
Reaction score
0
1EC5D0B7C.png



Can someone explain me how one term got to the other term? It makes no sense to me
 

Attachments

  • wtf.png
    wtf.png
    4.2 KB · Views: 482
Mathematics news on Phys.org
tahlaskerssen said:
1EC5D0B7C.png



Can someone explain me how one term got to the other term? It makes no sense to me



Your image is not publicly accessible. Can you change its permissons?
 
NascentOxygen said:
Your image is not publicly accessible. Can you change it's permissons?

I uploaded it.

By the way, he said something about "factoring sums out" what is that supposed to mean? This is the first time I've ever encountered something like this and i have taken up to differential equations regarding my math level.
 
The expression is of the form: A. ln Q - A. ln w
where A is a long summation and common to both terms.

Besides A, ln Q is the other term inside the first summation (likewise, besides A, you can see that ln w is the other term in the second series).

As each summation is over the same range, then you can combine the two series in one, using just one sigma.

Then combine the terms into one making use of: ln Q - ln w = ln (Q/w)

finally remember: ln (Q/w) = - ln (w/Q)

It looks forbidding, but really isn't. :wink:

Basically, write the expression without the ∑ symbol, and simplify what you see.

EDITED
 
Last edited:
i'm so stupid.. i deserve to go start college again.. Thanks a lot man!(honestly, i didnt know you could combine two same series into one, i was just treating them as a normal number and they were cancelling each other or getting a sigma squared, lol)
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top