Results 1 to 9 of 9

- July 13th 2007, 01:17 PM #1

- Joined
- Jul 2007
- Posts
- 6

## 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, 02:16 PM #2

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

- July 13th 2007, 02:37 PM #3

- July 13th 2007, 03:16 PM #4
Here is the image ImageShack - Hosting :: graphdz9.png]

- July 13th 2007, 03:52 PM #5

- July 13th 2007, 10:08 PM #6

- July 14th 2007, 05:15 AM #7

- July 14th 2007, 07:26 AM #8

- Joined
- Jul 2007
- Posts
- 6

## 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, 06:34 PM #9

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

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.