Is there a formula to get x in Excel without using solver: 0.5^x+0.2^x+0.25^x=1

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Discussion Overview

The discussion centers around the equation 0.5^x + 0.2^x + 0.25^x = 1, specifically exploring whether there is a formula to solve for x in Excel without using the Solver tool. The scope includes mathematical reasoning and potential computational methods.

Discussion Character

  • Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant states the equation 0.5^x + 0.2^x + 0.25^x = 1.
  • Another participant expresses doubt about the existence of a neat formula for x.
  • A different participant claims there is no analytic solution and suggests that an iterative approach is necessary, mentioning methods like using the Solver, writing a macro, or employing the Newton method in Excel cells.
  • A final participant acknowledges the previous points with agreement.

Areas of Agreement / Disagreement

Participants generally agree that there is no straightforward formula for x and that iterative methods are required, but there is no consensus on a specific approach or method to use.

The Investor
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TL;DR
Hi! I wanted to see if there is a formula to get x in excel without using solver: 0.5^x+0.2^x+0.25^x=1. Thanks!
0.5^x+0.2^x+0.25^x=1.
 
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I don't think there is a neat formula for x.
https://www.wolframalpha.com/input/?i=0.5^x+0.2^x+0.25^x=1

1602626567806.png
 
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There is no analytic solution to it and it's not a standard problem, so you need some sort of iterative approach. You can do that with the solver, you can write a macro to do it, you can even do it in some Excel cells (e.g. using the Newton method), but Excel won't have a nice formula for it.
 
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Likes   Reactions: berkeman
OK, that's what I thought. Cheers guys.
 

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