Germany| A Nice Math Olympiad exponential problem. | Can you solve this?

This is a Nice math Olympiad exponential question. The solution was obtained by applying the laws of exponential or indices. #matholympiadproblem #mathematics #exponentialequations

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[@Extratremendouszeus]

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[@prime423]

Correct!sUsing synthetic division,the other two roots can easily be found. Any mathlete would solve this in a minute or two.

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[@marcgriselhubert3915]

y = 2^x. We have y^3 + y^2 - 36 = 0, y = 3 is an evident solution then we can factorize: (y -3).(y^2 + 4.y +12) = 0 The equation y^2 + 4.y + 12 = 0 has no real solution (delta< 0), so y = 3 is the only solution. Then 2^x = 3 and x = ln(3)/ln(2) is the only real solution of the given equation.

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[@moonwatcher2001]

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[@RyanLewis-Johnson-wq6xs]

Input 4^(log(2, 1.5) + 1) + 8^(log(2, 1.5) + 1) = 36 Result True x=Log[2,1.5]+1

[@teofilodaquipil4100]

NX=8/5 When I saw the equation, I don't need paper and pencil. I got the answer in less than 1 minute. No need to apply log.

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[@youngdkout]

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[@anasanasa645]

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[@RyanLewis-Johnson-wq6xs]

I did it in my head.

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[@mitradhulipala449]

Lenghthy procedure...

[@EboBuabae-zz8my]

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[@SidneiMV]

4ˣ + 8ˣ = 36 2²ˣ + 2³ˣ = 36 (2ˣ)³ + (2ˣ)² = 36 = 3³ + 3² 2ˣ = u u³ + u² = 3³ + 3² u³ - 3³ + u² - 3² = 0 (u - 3)(u² + 3u + 9 + u + 3) = 0 (u - 3)(u² + 4u + 12) = 0 u - 3 = 0 => u = 3 2ˣ = 3 => *x = log₂3 = (1/ln3)ln2* u² + 4u + 12 = 0 => no real solutions

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[@eldoserenado458]

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