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?
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?
@@AnatolyGavr yes, I see your problem. When I multiplied in 8 I probably should have said it's 2^3. It's because we are working with ln 1/2 that we need to try powers of 2 and 1/2 but this part is tricky!
Prof.....please mention......with some special tricks.
You have nicely displayed the solutions !!!!!
Thanks! 🙏
By trying I found two solutions: x1=1 and x2=3
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?
Hi. Yes there is an infinite number of imaginary solutions to this. And one way to solve that equation is with lambert w 😃
This is Something new sir😊
Hi Skyfall. I did some videos on it before but it was mostly a couple years ago 👍
Every engineering student pullout his calculator after seeing this 😂😂 rather using property
😂
Plotting f(x)=2exp(x) -3x +1 with Geogebra, you will find two zero places: 1 and 3.
nice :)
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?
Hey adandap. 2 points of intersection: 1 and 3. I did it on desmos and it looks ok
@@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.
@@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.
@owlsmath Turns out I was being dumb. And now I've immortalised that in internet carbonite! 🤪
@@adandap ha! It's ok I do it all the time (but i try to delete it from the video usually)
To me a clean stepwise procedure must be printed prior to such teachings.Writtings... overwrittings& in between sweeping creates lot of misgivings.
So the process in the video is pretty confusing huh?
@@owlsmath I didn't understand, how did you find the second root -3? Where did the number -8 come from? Why not 4 or 20?
@@AnatolyGavr yes, I see your problem. When I multiplied in 8 I probably should have said it's 2^3. It's because we are working with ln 1/2 that we need to try powers of 2 and 1/2 but this part is tricky!
This is very complex solution.
Yep loving this one! 🎉 thanks for the suggestion!
the solutions were not only real, but positive integers.