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I'm trying to solve a bigger problem however I am stuck at this step:

How can I solve:

$ 2^x - x = 5 $

any hints/tips/steps please?

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    Thanks, I know the answer is obvious in this case and can be found via trial and error. I was just wondering if there is a more concrete method that could be used for cases when the answer is not obvious.2011-10-23

1 Answers 1

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As alluded to in the comments there is an integer solution. For the other solution is existence of a solution good enough? You can use the Intermediate Value Theorem on the function $f(x)=2^x-x-5$. It is negative at $x=0$ and positive at $x=-6$. So, somewhere in between the IVT says there must be a $0$. Or you can use Newton's method on $f$ to approximate the $0$ of $f$.