# Stuck on an equation involving powers - I only have 1 unknown

1. Apr 11, 2014

### Flucky

Hi all sorry the title couldn't be more descriptive.

I'm having a bit of a brain block with this equation (it's the very end of a problem).

N($\frac{5}{6}$)$^{N-1}$ > $\frac{27}{5}$

My line of thought was to get the first N in terms of the power N-1..

How do I find N?

2. Apr 11, 2014

### dirk_mec1

Analytically you can't.

3. Apr 11, 2014

### Flucky

Sorry I meant how do I simplify the inequality, ie N > #

4. Apr 11, 2014

### SteamKing

Staff Emeritus
What dirk_mec1 said.

However, a comment in the OP raises a question: is the coefficient N the same variable as the exponent N? You seem to imply that they are different.

5. Apr 11, 2014

### Flucky

Ah I guess I've gone wrong somewhere.

Yes the N's are the same.

6. Apr 11, 2014

### micromass

Staff Emeritus
Is $N$ supposed to be an integer?

7. Apr 11, 2014

### Flucky

It represents the rolls of a dice. I'm going to post the full question over in the physics homework subforum.

8. Apr 11, 2014

### micromass

Staff Emeritus
Then it suffices to solve it by trial and error. An easy method is to graph the equation $y=x\left(\frac{5}{6}\right)^{x-1}$ with a calculator. That way the value(s) of $N$ that satisfy the OP will become clear. Once you found a suitable candidate for $N$, you can rigorously prove that this $N$ is a good candidate by just plugging it in the equation and calculating manually.

There is no way to solve the equation analytically, so you will need to resort to trickery such as the above.

9. Apr 11, 2014

### Flucky

10. Apr 11, 2014

### Ray Vickson

Actually, if the problem is truly as given in the above link then the solution will involve even more hassle that what you have now. Why would you think the solution is "easy"? What do you have against plotting graphs or against using numerical methods?