A Nice Logarithmic Equation x^(log(2x))=5

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[titassamanta]

Hope that you regain your energetic voice soon. Hats off to your efforts and commitment. Stay safe. Pray for your early recovery.

[snejpu]

Cancellation of a square root is sheer beauty and class. I didn't find it actually, had to cope with complicated expressions and made a mistake finally. : ) But this is really cool, when you see it.

[WahranRai]

1:09 By expanding and regrouping terms : y(y + log2) = log5 = log(10/2) = 1-log2
y^2 + ylog2 - 1+ log2 = 0
y1 = -1 (obvious root) then y2 = 1 - log2 = log5 because y1*y2 = -1 + log2 implies
y1= logx = -log10 = log (1/10) then x1 = 1/10 and y2 = logx = log5 then x2 = 5

[lambertquesada]

first multiply both sides by 2..

2x^log 2x=10

take log to both sides..
log2x^log2x=1
so, log 2x=+-1... then everything will follow...

[musicsubicandcebu]

The quadratic's the thing wherein you'll find the solution to the thing!

[anongrealistic]

Thank you, man. Especially for your effort.

[Daniel_Frise]

I really enjoyed this problem. Never considered using the identity 1=log10 to sums with other logarithms until now.

[turkishwagnerian]

Hocam sesin çok cansız çıkıyor. İnşallah hasta değilsindir. Aman dikkat et yaban ellerde kendine. Sen bizim gibi matematik sevdalılarına çok lazımsın 🤩

[trtlphnx]

You Sound GREAT ~
Love Your Channel and Thanks For The Knowledge ~

[guidemath]

If we write middle term log2y=(1-log5)y you can factorise directly as(y+1)(y-log5)=0

[PegasusTenma]

I found your voice, it’s hiding in a math textbook

[pk]

The only fine point that I would make is that when you take the square root of u^2 you get the absolute value of u . Of course I know that you know that . I only mention this because when you take the square root of (log2-2)^2 you should get absolute value(log2-2)=2-log2 because 2 is greater than log2 . It did not matter in your solution ; but, in some problems it will trip you up.

[MOROCCANFREEMIND]

Multiplying both sides by 2 then put log, will get the solution much easier

[juanmolinas]

hi Syber!, great solution!, you sound a litle tired...

[yuranasu]

We could just look carefully and see that 1 - log5 = log 2, which is well-known coefficient rule. If a + c = b, then one of the solutions should be - 1 and the second -c/a

[yoav]

Nice, the voice is gone but the math is still there!😃 wish you find your voice soon

[alexspadini]

Multiply both sides by 2 and then take the log… massively easier as you get (log2x)^2=1

[michaelpurtell]

initially started with the approach of the video but about 3/4 the way through noted that log 10 is one, 10 is 2x5 and so 5 to the one equal 5 getting to the 1/10 was too much of a challenge as did not see how to reduce the descriminant. as usual learned some useful lessions thanks

[kailashanand]

Aw man, hope you get better soon :)) you know you could always take a break right? Big ups man i love your videos :D

[noeticresearch]

Hope you feel better soon SyberMath. Great problem! 👍