solving an exponential triangle problem

[@oenrn]

For anyone wondering, the sides are √φ, φ, and φ√φ.

[@Justinr-12r]

tf are those symbols

[@metehan9185]

@@Justinr-12r this is phi. Phi is the angle of the z axis that is in the case used for the golden ratio phi = sqrt5+1/2

[@matt-fitzpatrick]

That is so cool that phi does that

[@HappyGardenOfLife]

@@metehan9185 Shouldn't that be sqrt5/2 + 1/2?

[@furezuu]

@@HappyGardenOfLife Probably they forgot to put parethesis there

[@ednk5054]

"No complex triangles here" So funny dude, got my like))

[@dwagonyt]

Love the video, quick suggestion: Could you solve a right triangle with sides: sin(x), cos(x), and tan(x)? Let me know!

[@meurdesoifphilippe5405]

Two cases are possible : if tan is the hypotenuse then tan^2 = sin^2+cos^2=1, and sine and cosine >0 so x=π/4 +2kπ.

[@dwagonyt]

@@meurdesoifphilippe5405 hey thanks so much for that; I’m not the most mathematically fluent but when you say tan^2 I’m assuming you mean tan^2(x) and same with the other functions, and for the solution for x, what is k? Thanks!

[@dwagonyt]

Still though, I would love to see a video on that !

[@emm3rsk]

@@dwagonyt k is any integer you want

[@degenerationz9284]

@@dwagonyt k∈Z

[@kaistrandskov]

This just blew my mind. Someday I'd love to see the connection between phi, e, pi, and i. But for now, my mind is blown for the day. thank you!

[@UnPackedWolf]

Honestly it feels so good to be able to solve this

[@Dalton1294]

Another way to write the answer is (ln(1+√5)-ln2)/2

[@gangsterbob007]

With school coming up I gotta watch more of these and hope I'll understand one some day

[@pad-dydrummer5929]

I will never be able to use two markers so conveniently haha! 😀😀🔥🔥 Crazy one as usual!

[@shruggzdastr8-facedclown]

I've seen double-ended markers before (one color at one end and a different one at the other)

[@SuperYoonHo]

Wow this fits perfect with my morning(all-day) math i homeschool (don't go to school) with your videos and those help really a lot. Thanks mate and hope (wish) you would get many_subscribers!(factorial)

[@debdami]

the hypothesis that e^x e^3x ?

[@samwalko]

I remember seeing a problem with a very similar answer quite recently on some other math channel. Edit: nope actually, oops. It was this channel a couple weeks ago, with e^x + e^2x = e^3x. Solutions are just double what they are here.

[@saharhaimyaccov4977]

Do it for sin(x) - sin(2x) - sin(3x)

[@StanLiao]

"My name has two e's." I count 3 e's in "blackpenredpen" 😁.

[@dean532]

Yea, where do you get your T-Shirts from? 😅

[@user_08410]

omg i got the same answer but the method are a little different

[@ladripper47874]

2:50 why does he not proceed with making it 1+e^2x-e^4x=0 and then rearranging to -(e^2x)^2+e^2x+1=0 and continue from there? I'm not terrible great at math, but I feel like I have an error somewhere

[@Selim_Osmanli]

Thank you very much goodsir all respect and aprishiation, love your videos keep them up 💥🥳

[@Serghey_83]

e^(2x) =φ = [1 + sqrt(5)] / 2 a = exp(x) = φ^(1/2) b = exp(2x) = φ c = exp(3x) = φ^(3/2)

[@user-wu8yq1rb9t]

I'm big fan of *i* . Nice ..... Thank you Teacher ❤️

[@sphakamisozondi]

I'm a big fan of π

[@user-wu8yq1rb9t]

@UCesJUCFKPvBq6Mnr821C3dA I like *π* too and also *e* but complex numbers are another thing to me .... *It's shrouded in mystery*

[@metehan9185]

2:36 why cant we do 1+e^2x-e^4x = 0 ?

[@dwagonyt]

He is trying to break up the exponent of e^(4x) into e^(2x)^2, but of course you could just bring it to the other side and say: -e^(2x)^2 + e^2x + 1 = 0 and use the quadratic, however a negative a value doesn’t always look the neatest, that’s all

[@metehan9185]

@@dwagonyt thanks

[@dwagonyt]

@@metehan9185 no problem

[@mryjunior9391]

Hi, isn't the solution at the end meant to be x = ln(sqrt(phi))? Because e^2x is the same as (e^x)^2 so you have to square root first then natural log. Just curious, great video otherwise Edit: just realised ln(sqrt(phi)) can be written as ln(phi)/2 (because of logarithm power rule) sorry about that

[@lukasstanik1107]

Unless I am missing something, isn't it what he got at the end? Check 4:56

[@mryjunior9391]

@@lukasstanik1107 ye you're right I forgot to edit the reply ln(sqrt(phi)) can be written as ln(phi)/2 my bad

[@pimpaovieira]

Professor, can you make a class, Explaing how to solve cubic equations? Sorry, I dont speak inglish very weel... I am brazilian!!

[@ccbgaming6994]

Hey, I was wondering if you or any of the smart people in the comment sections can help with a math problem. 5^x + 6^x + 7^x = 8^y + 9^y + 10^y There should be an infinite number of solutions that can be found by an equation (y = …) that can be made from this one. The question is what is the equation. There should only x’s on the other side

[@perfectsinister2856]

in which set of numbers is x and y defined?

[@ccbgaming6994]

Real

[@Pratyush_jha590]

@@perfectsinister2856 real

[@aerodataspace4244]

I love math, specifically quadratics

[@p12psicop]

1.27-12.73-45.42

[@williamhogrider4136]

That's very cool 🍺🍺🍻.

[@hans429]

Wen ever i see the prof, it means pain to my brain 🤣🤣

[@pranavamali05]

thnku

[@truejeffanderson]

Kepler's triangle

[@harshrajsinhsarvaiya3024]

I am watching this video at 2 am. Lots of love from India 🇮🇳❤️

[@zidanihamid7485]

Beautiful

[@dorol6375]

I got x=-goldenratio÷2

[@OptimusPhillip]

x=ln(φ)/2

[@ghiurcarobertnicolas5957]

Wait a bit…. e^6x/e^2x is e^3x not e^4x , is it not?

[@adibmustafa914]

6-2 is 4

[@IMAN_IIT_PATNA]

Lol 🙂

[@robertveith6383]

No, you wrote it wrong. e^(6*x)/e^(2x) = You must have grouping symbols.

[@oenrn]

When dividing powers with the same base, you subtract the exponents.

[@KingGisInDaHouse]

I was going to do something similar pun intended. I knew x wasn’t going to change and that if this was a real triangle x is greater than zero so for the purposes of solving for x you can just divide out the e^x on every side of the triangle. Now it’s a 1,e^x,e^2x 1^2+e^x*e^x=e^(2x)*e^(2x) 1+e^(2x)=e^(4x) U=e^2x 1+u=u^2 I skipped the work here because I knew that phi squared is phi plus one already I’m assuming you worked this out for your audience. u=phi or phiBar u=e^(2x) ln u=2x x=ln(u)/2 x=ln(phi)/2 x=ln(phiBar)… no bueno phi bar negative ln(neg) no existy in x€R

[@nimmira]

Just realized this... Canon EOS 7D's sensor's crop factor is 1.613, just 0.005 shy away from φ

[@mel_ha22]

OMG, I didn't understan the end part because I have never seen the In thing 😫😫

[@Grizzly01]

ln is the natural logarithm aka logarithm base e

[@hafizusamabhutta]

What's your name?

[@del66404]

👏👏👏👏👏👏

[@klementhajrullaj1222]

And if sinx, sin2x, sin3x, how is the solution?! 😀😉

[@hkayakh]

Two e’s in your name? But ‘just algebra’ Has one!

[@NoNameAtAll2]

"my name has 2 'e's" blackpEnrEdpEn - that's 3 :)

[@lassikokkonen5618]

Bruh you for got negative infinity

[@giuseppemalaguti435]

x=ln@/2

[@alejrandom6592]

Ahhh yes, ln(φ) also known as arcsinh(1/2)

[@adityakumargupta9730]

There are infinitely many values of x, for which this "exponential triangle" exists. x = (1/2) ln[(1 + Sqrt[5])/2] + (2 k Pi) i - where k is any integer. All the values above make (e^x) = √φ.

[@ItsPungpond98]

Learn Chinese with bprp

[@andreasobama9487]

what in the hell

[@YoutubeDOGGY-t5z]

Sorry, but there will be - e²x/e²x=1, e⁴x/e²x=e²x e⁶x/e²x =e³x

[@datarioplays]

When dividing, you SUBTRACT exponents. For example (2^8)/(2^3)=2^(8-3)=2^5