Before even viewing, I smell the obnoxious odor of Lambert's W function.
@SyberMath3 ай бұрын
🙃😜
@giuseppeimbimbo15553 ай бұрын
So did I 😒
@R007CarrotVUX3 ай бұрын
BRO SAME-
@almanduku9043Ай бұрын
😂😂
@NirDagan3 ай бұрын
After we guess x=2, we have to show that this solution is unique. Consider the function f(x)=x5^x. Note that for non positive x, f(x) is also non positive. and for positive x, f(x) is strictly increasing (no need to differentiate to see that). so there is a unique solution to our equation.
@schrysafis3 ай бұрын
That's what I thought of instantly.
@neilmccafferty58863 ай бұрын
Two is clearly one solution. About two seconds to notice that.
@wtspman3 ай бұрын
The prime factorization of 50 is 2*5^2. By 1:1 correspondence x = 2. It’s not “guess and check”.
@fahrenheit21013 ай бұрын
Yes it is. Your logic is only valid if we were looking for integers x.
@FisicTrapella3 ай бұрын
I did this. The following step is to know if there are more solutions; which is what Syber do at the end of the video. 👌
@dwm19433 ай бұрын
First impression: x = 2 is an obvious solution. If we sketch the graphs y = 5^x and y = 50/x it would seem there can only be the one intersection, therefore x = 2 is the only solution. Now I'll watch the video. I am sure there will be some subtlety that has escaped me. This is a wonderful channel.
@txikitofandango3 ай бұрын
It's clever to set y = 5^x, so y=50/x. The exponential function is increasing everywhere, and the rational function is decreasing everywhere, and both functions are continuous for x>0, so they have at most one point of intersection
@SyberMath3 ай бұрын
good point!
@dwm19433 ай бұрын
@@SyberMath Lambert is ruining my life
@scottleung95873 ай бұрын
I got x=2 right away, but I could sense Lambert's W function being used just by looking at the original equation.
@joyneelrocks3 ай бұрын
Why use Lambert’s W Function when you can easily express that 50 = 2 * 25 = 2 * 5^2, meaning x = 2. It’s a similar process relative to using the W(), but much faster 😑
@maxgoldman89033 ай бұрын
Because we’ve to confirm that 2 is the only solution. Sometimes we may get a complex solution via Lambert’s function. Taking derivative of x•5^x is to confirm 2 is the only real solution. This step is redundant if we’ve used Lambert’s function.
@@josepherhardt164 exactly. also Lambert W function would be useful
@Jonasz3143 ай бұрын
I don't quite get why you try to do this dance inside the W function. You can start from the start by saying 50 = 2*25, and recognize that 25 = 5^2. So you rewrite the equation as x * 5^x = 2 * 5^2 Since the function on the left side is trvially increasing, there's only a single solution for x > 0, you can immediately see that x = 2 is the solution.
@roberttelarket49343 ай бұрын
"t"(tea) or coffee. Ha ha I love it! Better than to "b" or not to be!
The function is strictly increasing and continuous, so it's invertible, so the obvious real solution is unique in the reals. But if you want complex solutions also, then lambert W is obviously the correct approach
@dawnwing85973 ай бұрын
x.5^x =50 Let x=1, 1x5!=40 Let x=2, 2x5^2 = 50 Just a easy sum, nothing complicated Until more than 5 terms come
@terryendicott29393 ай бұрын
Use Desmos and graph y= x*5^x - 50.
@joannasi83863 ай бұрын
I think we can also find the solution factoring the right side od the equation and easily proove the funtion is monotonic finding its derivative as always positive, what causes only one possibile solution found by factoring😁
@nasrullahhusnan22893 ай бұрын
x×5^x=50 --> 5×5^x=2×5² Thus x=2
@tanbw9223 ай бұрын
You can see it immediately that x=2.
@_Rainbooow3 ай бұрын
so damn easy
@syed33443 ай бұрын
x.5^x=2.25 x.5^x=2.5² x=2
@giuseppemalaguti4353 ай бұрын
x=W(50ln5)/ln5
@louf71783 ай бұрын
8:30 Go through all these * hoops * . Not "loopholes".
@chasmosaurus33 ай бұрын
Since x=2, you are on the upper real branch of the Lambert function. There is only one solution and it is real.
@xd195922 ай бұрын
Un un um!!
@Darisiabgal75733 ай бұрын
2 * 5^2 = 50 ho-hum
@rakenzarnsworld23 ай бұрын
x = 2
@RealPersistences3 ай бұрын
Seems like this is overcomplicating it to me..
@vladimirkaplun57743 ай бұрын
🤑
@SyberMath3 ай бұрын
😜
@peskarr3 ай бұрын
f=x*5^x is monotonically increasing, so here is only one solution, and it is x=2 obviously, why does video last 10 minutes?
@LucasLee-vq2lv3 ай бұрын
if he replace the 5 with a 4, people should complain that it is not a whole number. The video is titled Can We Solve a Nonstandard Equation and he used a method that should work for any numbers. The video is not titled how to solve this specific equation; it is just how to solve this type of equation.
@roberttelarket49343 ай бұрын
"t"(tea) or coffee. Ha ha I love it! Better than to "b" or not to be!