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

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?

dirk_mec1
Analytically you can't.

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

Staff Emeritus
Homework Helper
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.

Flucky
Ah I guess I've gone wrong somewhere.

Yes the N's are the same.

Staff Emeritus
Homework Helper
Is ##N## supposed to be an integer?

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

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

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.

Homework Helper
Dearly Missed
Thanks but I have probably just messed up somewhere, as I don't think it will be that much hassle.