# Help transposing formula

1. Jul 15, 2013

### Colnago

1. The problem statement, all variables and given/known data

Hi, I'm looking through Roarks Formulas for Stress and Strain and I am having difficulty following one of the examples. Unfortunately my maths isn't as good as I would like. Hopefully someone can explain to me the steps taken to find the solution.

2. Relevant equations

The book states the following expression:

4.4661/n - 2(2.331)1/n + 1 = 0

From this it finds n = 2.86, unfortunately only the answer is given an no explanation. Can someone help?

Thanks

2. Jul 15, 2013

### HallsofIvy

Staff Emeritus
There is no simple "algebraic" method to combine 4.4661/n and 2.3311/n so no simple "algebraic" method to solve that equation. You could do it graphically or using some numerical method such as Newton's method. And "2.86" is only an approximate solution, not exact.

3. Jul 15, 2013

### Ray Vickson

For the solution of the problem *exactly as it is written*, Maple 14 gets n = 2.822595780, which rounds off to n ≈ 2.82 (NOT 2.86). If we assume, instead, that the equation should really by
$$(67/15)^{1/n} - 2(7/3)^{1/n} + 1=0$$
the solution becomes n = 2.795724837, which rounds off to n ≈ 2.80 (again, NOT 2.86).

Note: Maple uses numerical methods to solve such equations.

4. Jul 15, 2013

### SteamKing

Staff Emeritus
Roark is an old, old text which has several editions. When the equation in the OP was originally solved, the author (or one of his students) might have been using a slide rule or a set of log tables and counting on his fingers and toes.

5. Jul 16, 2013

### HallsofIvy

Staff Emeritus
Hey, don't knock counting on your fingers and toes! I do it all the time.

6. Jul 16, 2013

### haruspex

In binary, I trust?