Expand Log(a+b): Tips & Ideas

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In summary, the conversation discusses how to expand a given equation and the possibility of simplifying it. The question is raised of how to plot the two variables involved as a straight line graph, and the idea of taking the log of one variable and graphing it along with the other is suggested. It is noted that this may not give a formula, but it could help find a regression. The conversation then goes on to discuss the possibility of transforming the equation into a y=mx+c form and the context of the problem at hand.
  • #1
Saoist
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anyoen know how to expand this? i can't think of any obvious way...
 
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  • #2
What kind of result are you looking for - functions of a and b separately? As it stands, it is as simple as possible.
 
  • #3
There's not much you can do. In some cases, it's useful to factor it as [tex]\log a+\log(b+1)[/tex], but in general there's nothing simpler than the way you wrote it.
 
  • #4
i have a deceptively simple question you see:

X^3 = (cY+d)^2

where c and d are constants, with x and y the variables. how would you plot the 2 variables as a straight line graph. I'm having an idiocy attack and can only think "log it..."
 
  • #5
Take the log of Y and graph x, log y.
 
  • #6
that doesn't plot that relationship as a straight line though does it?

i was under impression you had to transform [said equation] into a y=mx+c type form
 
  • #7
Saoist said:
that doesn't plot that relationship as a straight line though does it?
i was under impression you had to transform [said equation] into a y=mx+c type form

You can't plot things like [itex]x^3=y^2[/itex] as a straight line on a normal graph.
 
  • #8
I didn't mean that would give you a formula, but if you had a set of data, you could find the regression by plotting x, log y. It's not the answer but it's a way to get it.
 
  • #9
Saoist said:
that doesn't plot that relationship as a straight line though does it?
i was under impression you had to transform [said equation] into a y=mx+c type form

No, none of log-log, log-linear or linear-log will make that equation a straight line.

What's the full context of the problem, do you have a number (more than 2) of x,y points and you wish to find constants c and d that give the "best fit" in some particular sense?
 

1. What is the formula for expanding Log(a+b)?

The formula for expanding Log(a+b) is Log(ab). This means that the logarithm of a sum is equal to the sum of the logarithms of the individual terms.

2. Can you show an example of expanding Log(a+b)?

Sure! Let's say we want to expand Log(3+5). Using the formula from the previous question, we can rewrite this as Log(3x5). Then, we can further simplify this to Log(15).

3. Are there any rules or tips for expanding Log(a+b)?

Yes, there are a few rules that can make expanding Log(a+b) easier. Firstly, you can only combine terms with the same base. Also, when expanding Log(a+b), the coefficients in front of the logarithms can be brought down as exponents on the individual terms.

4. How can expanding Log(a+b) be useful in problem-solving?

Expanding Log(a+b) can be useful in solving logarithmic equations or simplifying complex expressions involving logarithms. It can also help in finding the inverse of a logarithmic function.

5. Is there a specific order in which terms should be expanded in Log(a+b)?

No, there is no specific order in which terms should be expanded in Log(a+b). However, it is often helpful to rearrange the terms in a way that makes the expansion easier to follow. Additionally, it is important to keep track of any constants or coefficients that may need to be brought down as exponents.

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