## Rearrange equation with power

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
themainadam
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### Rearrange equation with power

Hi all,

Is it possible to rearrange this equation in terms of n

an = b * ( (1-r^n) / (1-r) )

Its just beyond me!

a is always much greater than b in this case.

Thanks
Adam

stapel_eliz
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### Re: Rearrange equation with power

Is it possible to rearrange this equation in terms of n

an = b * ( (1-r^n) / (1-r) )
"Possible"? Yes. "Reasonably feasible"? No.

According to Wolfram Alpha, the "solution" is as follows:

. . . . .$n\, =\, \frac{a\,W\left(-\frac{b\,r^{\frac{b}{a(1-r)}}\,\log(r)}{a(r\,-\, 1)}\right)\, -\, a\,r\,W\left(-\frac{b\,r^{\frac{b}{a(1-r)}}\,\log(r)}{a(r\,-\, 1)}\right)\, -\, b\,\log(r)}{a\,(r\, -\, 1)\,\log(r)}$

...where "W(x)" is the Lambert W-function.

themainadam
Posts: 2
Joined: Tue Feb 04, 2014 11:31 pm
Contact:

### Re: Rearrange equation with power

wow!
I tried logs, differentiation, integration and all the other tricks I could barely remember from my school days 20 years ago - but there is no way I could have got there.
Thank you so much for taking the time to answer my question. It's interesting to learn something new about maths - I've never heard of the Lambert W-Function before.

Thanks again,
Adam

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