Solving the Log Identity Problem: Understanding the Daume Equation

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Homework Help Overview

The discussion revolves around understanding the Daume equation and its relation to logarithmic identities, particularly focusing on the functions log(y) = log(x^2) and 2log(x). Participants explore the implications of domains and piecewise functions in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the equivalence of the functions and question how to plot them for different values of x. There is exploration of using absolute values and piecewise definitions to reconcile the two forms of the logarithmic expression.

Discussion Status

Some participants have offered insights into the relationship between the functions, while others are questioning their assumptions about the domains and the nature of the piecewise function. There is a sense of progress as participants attempt to clarify their understanding.

Contextual Notes

There is mention of potential confusion regarding the domains of the logarithmic functions and how they relate to negative values of x. The original poster expresses uncertainty about the piecewise nature of the functions involved.

tahayassen
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Homework Statement



http://img39.imageshack.us/img39/4729/daumequation13275759907.png

Homework Equations



N/A

The Attempt at a Solution



Hmm... This is a tough one. I thought these two functions have been mathematically proven to be exactly the same? Does it have something to do with the domains? The piece-wise function part is totally beyond me. :(
 
Last edited by a moderator:
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Hi tahayassen,

Can you plot log y= (x^2) for negative x values? And y=2log(x)? How can you make them identical?

ehild
 
ehild said:
Hi tahayassen,

Can you plot log y= (x^2) for negative x values? And y=2log(x)? How can you make them identical?

ehild

Hmm... I suppose not. I guess for positive x values, I can use 2log(x), and for negative values, I can use 2log(-x) to make it look like log(x^2).

And to make log(x^2) look like 2log(x), I guess I can put the absolute value around the x^2 like so: log(|x^2|). Is this correct?
 
No, I've made a mistake

2log(|x|)=log(x^2)
To make log(x^2) look like 2log(x), you would just the positive x values.
 
I think I've answered my question.

I just want to confirm if the answer is right:

http://img51.imageshack.us/img51/1087/daumequation13275770432.png
 
Last edited by a moderator:
Yes, that correct.
 
tahayassen said:
I think I've answered my question.

I just want to confirm if the answer is right:

http://img51.imageshack.us/img51/1087/daumequation13275770432.png

You did this self-homework-helping job very well :biggrin: Congrats!

ehild
 
Last edited by a moderator:

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