Rearrange equation with power  TOPIC_SOLVED

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

Rearrange equation with power

Postby themainadam on Tue Feb 04, 2014 11:36 pm

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
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Re: Rearrange equation with power  TOPIC_SOLVED

Postby stapel_eliz on Wed Feb 05, 2014 12:20 pm

themainadam wrote: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:

. . . . .

...where "W(x)" is the Lambert W-function. :wink:
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Re: Rearrange equation with power

Postby themainadam on Wed Feb 05, 2014 2:47 pm

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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