# I An exponential number algebra problem

Tags:
1. Mar 17, 2019 at 4:38 AM

### Edge5

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.

2. Mar 17, 2019 at 4:51 AM

### Staff: Mentor

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?

3. Mar 17, 2019 at 5:01 AM

### Edge5

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: Mar 17, 2019 at 5:12 AM
4. Mar 17, 2019 at 5:05 AM

### BvU

So where are the $a$ and $b$ in your story ?

5. Mar 17, 2019 at 5:11 AM

### Edge5

In my question a and b were Linitial and Lfinal

6. Mar 17, 2019 at 5:15 AM

### BvU

So take logarithms ! $$\ln\omega = \ln A - 1.5\ln L$$

7. Mar 17, 2019 at 5:17 AM

### Edge5

I will try thanks