Stuck on equation for determining data structure

idlegoose

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Jul 3, 2019
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Hello all. I am developing data structure and was able to come up with a formula involving certain attributes.

All variables are integers >0

B and Y are variables about specific geometry of hardware.
C is also determined by hardware but can change for different hardware.


\(\displaystyle (2^{X} - 1)\cdot B+\sqrt{Y}\cdot (C^{X} - C^{X-1})= Y\)

*Latex is not displaying it correctly so here is the full parenthesized text also, this will display correctly if plugged into wolframalpha
((2^X) - 1)B+sqrt(Y)(C^(X) - C^(X-1))= Y

I am needing to solve for X but my college log/exponent factoring eludes me.

I got as far as \(\displaystyle (B2^{X})/(C-1) + C^{X-1}=(Y-B)/\sqrt{Y}(C-1)\)

If anyone has any tips or suggestions please feel free to comment.
 
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tkhunny

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Apr 12, 2005
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Yeah, you're not getting anywhere. The best you can hope for is to solve for AN X - either the one with the C or the one with the 2. Can't do both. You will have to resort to numerical solutions rather than strictly algebraic.
 

idlegoose

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Jul 3, 2019
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would it help if C is dependent upon B, such as C= B/16
((2^X) - 1)B+sqrt(Y)((B/16)^(X) - (B/16)^(X-1)) = Y
 

Subhotosh Khan

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would it help if C is dependent upon B, such as C= B/16
((2^X) - 1)B+sqrt(Y)((B/16)^(X) - (B/16)^(X-1)) = Y
The main problem of the given equation is non-linearity and that still
remains. I do not see any closed-form solution.
 
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