It's Lambert W time! (with some cheating)

For more info on the Lambert W function:
Introduction Video:
• Lambert W Function - I...
Playlist:
• Lambert W Function
Many practice problems:
owlsmath.neoci...
owlsmath.neoci...
My very primitive Lambert W Calculator (by Newton's Method):
owlsmath.neoci...
Check out my other channel:
/ @owl3math
Check out my other channel OWLS SCHOOL OF MATH!
/ @owlsschoolofmath9732
Website:
owlsmath.neoci...
#algebra
#lambert
#lambertwfunction

[@pspprabhat]

Prof.....please mention......with some special tricks. You have nicely displayed the solutions !!!!!

[@owlsmath]

Thanks! 🙏

[@akirakato1293]

btw for your final step of multiplying by a/a for a=2 or 8, if you set up the equation to solve for a you get a^3=2^(a+1) which im not sure how u solve it but it does have the 2 integer solutions we desire and wolfram alpha gives us an additional imaginary solution in terms of product log function which means the final solution for x also has an imaginary solution?

[@owlsmath]

Hi. Yes there is an infinite number of imaginary solutions to this. And one way to solve that equation is with lambert w 😃

[@reaperskyfall6691]

This is Something new sir😊

[@owlsmath]

Hi Skyfall. I did some videos on it before but it was mostly a couple years ago 👍

[@reaperskyfall6691]

Every engineering student pullout his calculator after seeing this 😂😂 rather using property

[@owlsmath]

😂

[@pspprabhat]

To me a clean stepwise procedure must be printed prior to such teachings.Writtings... overwrittings& in between sweeping creates lot of misgivings.

[@owlsmath]

So the process in the video is pretty confusing huh?

[@pspprabhat]

This is very complex solution.

[@owlsmath]

Yep loving this one! 🎉 thanks for the suggestion!

[@maxvangulik1988]

the solutions were not only real, but positive integers.

[@adandap]

I'm a bit confused about the two solutions, though they clearly both work. The graphs of 2^x and 3x-1 clearly have only point of intersection. Having sketched them and observing that x=1 works, I stopped. What am I missing?

[@owlsmath]

Hey adandap. 2 points of intersection: 1 and 3. I did it on desmos and it looks ok

[@adandap]

@@owlsmath Once you get to the multivalued W function, yes. But not if you plot y = 2^x and y = 3x - 1 to begin with.

[@owlsmath]

@@adandap sorry I think I must be missing something here. Want to email me a screenshot of what you see? I can email you mine.

[@adandap]

@owlsmath Turns out I was being dumb. And now I've immortalised that in internet carbonite! 🤪

[@owlsmath]

@@adandap ha! It's ok I do it all the time (but i try to delete it from the video usually)