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This equation clearly cannot be solved using logarithms.

$$3 + x = 2 (1.01^x)$$

Now it can be solved using a graphing calculator or a computer and the answer is $x = -1.0202$ and $x=568.2993$.

But is there any way to solve it algebraically/algorithmically?

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    I'm not sure why this question was downvoted. It seems like a legitimate question to me.2012-10-20
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    Are you familiar with the Lambert-W Function (http://mathworld.wolfram.com/LambertW-Function.html), hence see: http://www.wolframalpha.com/input/?i=Solve%5B3+%2B+x+%3D+2+%281.01+%5E+x%29%2Cx%5D2012-10-20
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    (I didn't downvote) maybe because there are similar problems already on here? I swear I've seen a few, but I just searched & turned up nothing, so I can't blame you for not finding one! Similar one: http://math.stackexchange.com/questions/61774/how-do-i-solve-this-equation-involving-a-logarithm2012-10-20

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