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

[Obelisk]

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.

 

[Mark44]

Square both sides.

 

[HallsofIvy]

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.

 

[Obelisk]

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.

 

[Mark44]

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?

 

[Obelisk]

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.

 

[Obelisk]

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!

 

[HallsofIvy]

I just wish I knew clearly what those problems were!