Math Olympiad | A Nice Algebra Problem | A Very Nice Exponential Equation

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Find the value of x?
How to solve 8^x+50^x=20^x+1
In this video, we'll show you How to Solve Math Olympiad Question A Nice Exponential Equation 8^x+50^x=20^x+1 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
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[@emmanueldias5571]

Nice good.

[@SALogics]

Thanks and welcome ❤

[@billv39]

I've seen this before in related problems on RUclips so you're not the first.
Y1 and Y2 are conjugates whose product is 1. Therefore Y2 = 1/Y1 and log(Y2) = -log(Y1). It therefore seems to me that a better final answer is X = ±log(10 + 3√11)/(log(2) - log(5)). Your numerical answers confirm this.
Others convert the final answer to base 2/5, which, though more compact, unnecessarily complicates things IMO. I'm pleased to see that you didn't do that.
I agree that this is a nice problem.

[@SALogics]

Thanks and welcome ❤