A nice Math Olympiad Exponent Simplification | How to Solve 4x=2^x | Lambert W Function in Action

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Math Olympiad Exponent Simplification | How to Solve 4x=2^x | Lambert W Function in Action #exponent#olympiad #simplification#exam
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30 май 2024

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Комментарии : 13

@bouzekriamir1539 21 день назад

Tank you professeur

@pspandey9737 22 дня назад

Thank you!!!

@superacademy247 22 дня назад

You're welcome!

@MrGeorge1896 28 дней назад

Nice problem. x = 4 is the trivial solution which doesn't need so much explication. I would propose to build the video around the peculiarities of the Lambert function W(x) so your viewers can understand how to use this function in order to get the second, non-trivial solution. (x = 0.3099...)

@superacademy247 28 дней назад

Absolutely! I am working on that. I would like to dive deep into Lambert W function. I want to create the best video that would let everybody understand clearly and precisely.

@detectiveandspynovels7140 28 дней назад

♥️♥️

@superacademy247 28 дней назад

Thanks 👍💯👍 your support

@user-xx3es5de8d 28 дней назад

Professor, o X é igual a 4, com certeza. Pois, 4 x 4 = 16 e 2 elevado a potência 4 = 2 x 2 x 2 x 2 = 16

@prime423 28 дней назад

You dont need lambert or any other trick. Just take the log of both sides with base 2!!

@detectiveandspynovels7140 28 дней назад

We do it need log but w function

@SidneiMV 28 дней назад

4x = 2^x (x)2^(-x) = 1/4 (-x)e^(-xln2) = -1/4 (-xln2)e(-xln2) = -(1/4)ln2 (-xln2)e(-xln2) = (1/16)(-4)ln2 (-xln2)e(-xln2) = (1/16)ln(1/16) -xln2 = W[(1/16)ln(1/16)] x = -(1/ln2)W[(1/16)ln(1/16)] a possible value for W[(1/16)ln(1/16)] is ln(1/16) so follows a possible value for x x = -(1/ln2)ln(1/16) x = -(1/ln2)(-4ln2) *x = 4*

@pspandey9737 28 дней назад

2^×=4×. =>2^×_2=× =>1=×.2^(2-×) =>-1=(-×)(2^2-×) =>2-1 =(2-×).e^(2-×)ln2 =>w{ln2} =w{ 9:57 (2-×)ln2.e^(2-×)ln2} [W(Ln2)=(2-×)ln2] =>×=[2-w(ln2)/ln2]

@pspandey9737 28 дней назад

Will you kindly point out the error in this solution please.!!