I An exponential number algebra problem

AI Thread Summary
The discussion revolves around the algebraic expression an - bn and the challenge of expressing it solely in terms of C and n, where C is defined as a - b. It is clarified that while an - bn can be factored to include (a - b), it cannot be completely expressed without a and b. A user introduces a context involving resonance frequency changes due to beam deformation, linking the variables to physical parameters like tensile force and Young's modulus. The conversation shifts to using logarithmic transformations to analyze the relationship further. Ultimately, the problem highlights the complexity of algebraic manipulation in both mathematical and physical contexts.
Edge5
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Let a,b,c and n are real numbers.a-b = C
I want to get rid of a,b and find the following expression in terms of C and n. How can I do that?
(an-bn)= ? (in terms of C and n)

Thank you.
 
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You can't.
Simple example: a=2, b=1 and a=1, b=0 both lead to C=1, but a2-b2 is different for the two cases.

You can rewrite an-bn to have a factor of (a-b) but you won't get rid of a and b completely.

What is the context of this question?
 
mfb said:
You can't.
Simple example: a=2, b=1 and a=1, b=0 both lead to C=1, but a2-b2 is different for the two cases.

You can rewrite an-bn to have a factor of (a-b) but you won't get rid of a and b completely.

What is the context of this question?

I have a resonator and the resonance frequency (w) of it is given by w=A(L-1.5) where A is a constant and L is the length. When I apply a force the resonance frequency changes because length of the beam changes due to deformation. I need to find the change in resonance frequency as a function of change in length.
That's why I said winitial = ALinitial-1.5
and ALfinal-1.5
Lfinal-Linitial = (Linitial.Ftensile)/(EAcrossection)
Where E is the young modulus and A is the area.
In my question a and b were Linitial and Lfinal
n was -1.5
C was (Linitial.Ftensile)/(EAcrossection)
 
Last edited:
So where are the ##a## and ##b## in your story ?
 
BvU said:
So where are the ##a## and ##b## in your story ?
In my question a and b were Linitial and Lfinal
 
So take logarithms ! $$\ln\omega = \ln A - 1.5\ln L$$
 
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BvU said:
So take logarithms ! $$\ln\omega = \ln A - 1.5\ln L$$
I will try thanks
 

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