How do you determine wavelength, x, from this expresstion?

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Homework Help Overview

The discussion revolves around a semiconductor problem involving the equation w = (50.12 x) ^ 0.5, where participants are trying to determine the value of x within the interval 0.5 < x < 2.5. The original poster seeks a mathematical method to find x, which is described as the minimum practical value for the solution.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants suggest squaring both sides of the equation and dividing by 50.12 as potential methods to isolate x. However, the original poster expresses concern that these methods do not yield the desired value of x. There is also a mention of wanting to find the interval for w based on the given range of x.

Discussion Status

The discussion is ongoing, with various approaches being explored. Some participants have provided guidance on manipulating the equation, while the original poster is seeking further simplification and clarity on expressing the equation in terms of x. There is no explicit consensus on the best method yet.

Contextual Notes

The original poster notes that the value of w is unknown and that the solution must adhere to the physical constraints of the problem. There is also a mention of a different approach involving another equation that the original poster wishes to simplify.

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Homework Statement



The problem is a semiconductor question which I have resolved and gotten the equation:

w = (50.12 x) ^ 0.5

From the knowledge of this system, x is in an interval such that 0.5 < x < 2.5

What mathematical method of solution would help find the solution to this equation? The value of x is supposed to be the minimum practical value for the solution.

Thanks.
 
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Obelisk said:

Homework Statement



The problem is a semiconductor question which I have resolved and gotten the equation:

w = (50.12 x) ^ 0.5

From the knowledge of this system, x is in an interval such that 0.5 < x < 2.5

What mathematical method of solution would help find the solution to this equation? The value of x is supposed to be the minimum practical value for the solution.

Thanks.
You solve an equation by "backing out". Since the last thing done or the right was "0.5 power", which is the same as square root, so the opposite: square both sides. Then you are left with just 50.12x on the right. Since x is multiplied by 50.12, do the opposite: divide both sides by 50.12.
 
Thanks for your ideas so far.

Well, by squaring it and/or dividing it by 50.12, I am not going to be able to obtain the value of x still which should be in the interval 0.5 < x < 2.5 (from the theory of the physical problem).

The value of w is unknown and the only way of finding it is by solving for this equation.

Thanks again.
 
Apparently you want to find the interval for w if 0.5 < x < 2.5 in this function:
w = (50.12 x) ^ 0.5

I interpreted your original post as wanting to find x.

The function above is an increasing function, meaning that as x increases, so does w. On the interval 0.5 < x < 2.5, the smallest value of w will be for x = 0.5; the largest value for w will be for x = 2.5.

Is that what you're looking for?
 
Thank you all for your help so far.

Well, I have used another approach in resolving this this problem but I am wondering if anyone could suggest a way to simplify this further. I wish to express this equation in terms of x:

d = 10^-20 x^(-18/4) x^-1.

So, is there a way to write this equation in the form: x = ... ??

I have checked my solution with numeric values which seems fine but I need to express in that form, please help. Thanks.
 
To Mark44, HallsofIvy and other members who helped or looked into my posting, thanks so much!

The good news is I finally resolved the problems and I am so glad I can now move on!
 
I just wish I knew clearly what those problems were!
 

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