smeag0l:
You cant leave the answer as a function because that is actually not the answer. You have to evaluate it with a program like wolfram alpha. The Lambert W function usually has two solutions for all negative values greater than -1/e. The result is usually a product logarithm and if any of you had left the answer in the form a a product logarithm you would have gotten it. The last four lines of your solution were incorrect while mathslord's solution had the last two lines of his own solution as incorrect.

Ikennablue:
please can u show the working of the number one question??

Ikennablue:
I've not heard of all this wolfram alpha and lambert W function before.
I thought the beauty of mathematics is that you can use any method as far as you arrive at the final answer??
If am in a competition, I only need to look at the number one question to know that x is equal to 2.

Mathscum:

That's exactly what I did in my solution I evaluated with wolfram alpha it gave me one value.
I am surprised when you say my solution is dubious.

dprpikin:


With what you wrote here, it means it cannot be evaluated ordinarily without the use of a computer program. In that case, graphical method remains the easiest way to solve it.

smeag0l:
I didnt look at it because it was sent in after the challenge had closed.

smeag0l:
On the contrary, numerical approximation methods like newton-raphson will give you the two correct answers(with some help on how continuous monotonic functions work). In my case, I was trying the graphical method and I found the first derivative of the function f(x)=2^2x-8x and equated it to zero to get the value of x which is 1.264. Then I found f(1.264) which gave a negative value of -4.34. This gave me some other information-The function has two roots which lie on the left and right hand side of x=1.264. I also found the y intercept by f(0) which gave 1. I abandoned the more complicated graphical solution in favour of the easier numerical approximation since I have known the nature of the function.The newton-raphson's method gives the two roots i.e x=0.155 and x=2.

dprpikin:


Ok. I'll try the graphical method with the little I know.

smeag0l:
Better. I'm also completing that graphical solution now and may post it here if people want.

smeag0l:
Better. I'm also completing that graphical solution now and may post it here if people want.

Mrshape:

I did they graphical to get my solution too.
Because I don't have paid wolfram alpha.,
That's I I got my two values for my solution
The constant value of omega of that function gave one solution.
So I use graph yo evaluate and zoom.
Anyway it was a nice challenge.
What I want to learn from you is how to get the omega value without program

smeag0l:
Your graph isnt correct. The result is a parabolic graph with a y intercept of 1.

smeag0l:
Where is the graph?Wolfram alpha is free. There are other tools like mathcad that is not a program but a calculation software you can use to arrive at the answer too.

smeag0l:
For those of you I have contacted to send your account numbers and haven't sent , I need it urgently as I may be forced to move on to the next fastest person with a correct answer if you don't respond. Please check your emails urgently.

smeag0l:
For those of you I have contacted to send your account numbers and haven't sent , I need it urgently as I may be forced to move on to the next fastest person with a correct answer if you don't respond. Please check your emails urgently.

smeag0l:
This is not it. I'll post it shortly as I have completed the graphical one.

smeag0l:
This is not it. I'll post it shortly as I have completed the graphical one.

smeag0l:
This is not it. I'll post it shortly as I have completed the graphical one.

Mrshape:

Those are my graphs I used
I will like to see yours

Mrshape:

I also used this

smeag0l:
Yeah, these are used to obtain the zeros of the func4ion before plotting it on a single curve. I have posted the solution here. I will not post the newton-raphson one because I have already said one of the winners will post that.

Mrshape:

Alright but how were you areble to read that graph to 4 dp?

Mrshape:

Snap this paper again it is not clear