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- July 13th 2007, 12:17 PM #1

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## x^2 + 1 = 2^x; solved for x??

hi there,

i've come to an impasse on this one

would like to solve it for x and have tried

manipulating logs and all sorts of things.

by the way i know the answer is 1

i just want to know if the equation

can be stated in terms of x.

thanks,

poly

- July 13th 2007, 01:16 PM #2

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- July 13th 2007, 01:37 PM #3

- July 13th 2007, 02:16 PM #4
Here is the image ImageShack - Hosting :: graphdz9.png]

- July 13th 2007, 02:52 PM #5

- July 13th 2007, 09:08 PM #6

- July 14th 2007, 04:15 AM #7

- July 14th 2007, 06:26 AM #8

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## thanks

wow,

thanks for all the quick responses! i will

be back to this forum in the future i'm sure.

glad it was not just my still shaky abilities

contributing to the lack of a solution.

is there some theorem or theory which

would say definitively whether there is

or is not an analytic solution to my

particular question?

thanks again,

poly

- July 14th 2007, 05:34 PM #9

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You can create your own non-elementary functions to create solutions.

So for example,

for

Has solutions via "Lambert W function", that is an analytic solution.

Same here we can create the "Hacker Z function" of whatever you call it and solve:

Or something like that.

But it will not be one of those standard "nice" functions.