# One equation one unknown

1. Feb 10, 2008

### sara_87

1. The problem statement, all variables and given/known data
i want to find the value of k in the following equation:
8.7-(0.75/k)=[e^(8k)](11.7-(0.75/k))

2. Relevant equations

3. The attempt at a solution

i know i can use matlab but i dont have matlab and i dont even know how to do it on matlab; does anyone know how to do it on matlab?
is there an alternative method to find k?

thank you

2. Feb 10, 2008

### Dick

If you don't have any special tools, write the problem as f(k)=exp(8*k)*(11.7-.75/k)-(8.7-0.75/k). Now you want to find where f(k)=0. Now graph it and look for a zero, or just try different values of k until you find one where f(x) is positive and one where it's negative. E.g. f(0.03)<0 and f(0.04)>0. That means there is a root between 0.03 and 0.04. Try the midpoint k=0.035 and keep refining the interval containing the root until you get enough significant digits for the needs of the problem. This is called 'bisection'.

3. Feb 10, 2008

### sara_87

yes i know that method but it takes too long and i'm lazy.
i just need the answer without the working out so i dont want to take too much time finding the value for k.

4. Feb 10, 2008

### cristo

Staff Emeritus
Well, you should just probably wait until you get to a computer with maple or matlab or whatever. Otherwise, you'll need to do it the long way!

5. Feb 10, 2008

### HallsofIvy

Staff Emeritus
There is no simple formula for such a problem. You might be able use the Lambert W function, but I suspect just getting it into the right form for that would be much more work that the graph Dick suggested.

6. Feb 11, 2008

### sara_87

yes but how do i type that into matlab and how do i find k using matlab? what do i type?

7. Feb 11, 2008

### EnumaElish

8. Feb 11, 2008

### HallsofIvy

Staff Emeritus