- #1
How is this equality possible? What did the professor do to reach it?
- Context: Undergrad
- Thread starter tahlaskerssen
- Start date
-
- Tags
- Professor
Click For Summary
SUMMARY
The discussion centers on the mathematical manipulation of the expression A. ln Q - A. ln w, where A represents a summation common to both terms. The key technique discussed is "factoring sums out," which allows for the combination of two series into one using a single sigma notation. This simplification leads to the expression ln (Q/w), which can further be expressed as -ln (w/Q). The participants clarify that understanding this process is crucial for simplifying complex mathematical expressions.
PREREQUISITES- Understanding of logarithmic properties, specifically ln(Q/w) and ln(w/Q)
- Familiarity with summation notation and sigma (∑) operations
- Basic knowledge of algebraic manipulation techniques
- Experience with differential equations or advanced mathematics
- Study the properties of logarithms in detail, focusing on their applications in algebra
- Learn about summation techniques and how to combine series effectively
- Explore advanced algebraic manipulation methods for simplifying expressions
- Review differential equations to reinforce understanding of mathematical concepts
Students in mathematics, particularly those studying algebra and calculus, educators teaching advanced math concepts, and anyone looking to improve their skills in simplifying complex mathematical expressions.
- #2
NascentOxygen
Staff Emeritus
Science Advisor
Homework Helper
- 9,253
- 1,080
tahlaskerssen said:
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?
- #3
tahlaskerssen
- 10
- 0
NascentOxygen said:
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.
- #4
NascentOxygen
Staff Emeritus
Science Advisor
Homework Helper
- 9,253
- 1,080
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.
Basically, write the expression without the ∑ symbol, and simplify what you see.
EDITED
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.
Basically, write the expression without the ∑ symbol, and simplify what you see.
EDITED
Last edited:
- #5
tahlaskerssen
- 10
- 0
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)
Similar threads
- · Replies 25 ·
- · Replies 4 ·
- · Replies 58 ·
- · Replies 7 ·
- · Replies 4 ·
- · Replies 4 ·
Undergrad
De-dimensionalizing/rescaling units
- · Replies 6 ·
- · Replies 14 ·