solving (2^x) = (x^3)

[agrimm2]

hello



yeah so basically i was wondering if anyone could show the steps involved in finding the value of x. I tried using log2 but got stuck. thanks

 

[Romsek]

There's no simple closed form solution for this unless you all are studying the Lambert W function. Are you?

 

[skeeter]

 

[Cubist]

There's also another solution at x ≈ 9.9395351414269

EDIT:You can see this on the far right of @skeeter 's graph - it has a very steep gradient and therefore it almost looks like a border of the image!

 

[skeeter]

spread to see both zeros ...

 

[Steven G]

I knew that there had to be more than 1 solution. This is a problem for bprb!

 

[Steven G]

hello

View attachment 24680

yeah so basically i was wondering if anyone could show the steps involved in finding the value of x. I tried using log2 but got stuck. thanks

There is no easy way to solve this algebraically. I would graph both functions to get an idea where the roots might be and then use the intermediate value theorem to zoom in on those roots.

 

[Cubist]

This is a problem for bprb!

I'll bite, and show my ignorance, what or who is bprb? Could it be Ballpark Bob ?

 

[Steven G]

I'll bite, and show my ignorance, what or who is bprb? Could it be Ballpark Bob ?

I was waiting for that question. There is a youtuber who has solved problems like this one. He write with a Black Pen and a Red Pen while holding both in his hands and switches between then flawlessly.

 

[Romsek]

but can bprp do this?

 

[Steven G]

but can bprp do this?

Nobody can do better than Dr Walter Lewins, nobody. The man is a legend.

It is absolutely insane that this professor has over 50 million views on this video. The video has almost 100,000 comments. Dr Lewins really must be a legend. Future MIT students lost out when he retired.

 

[lookagain]

He write with a Black Pen and a Red Pen while holding both in his hands and switches between then flawlessly.

He holds both in the same hand and switches between them flawlessly.

 

[lookagain]

He write with a Black Pen and a Red Pen while holding both in his hands and switches between then flawlessly.

He holds the black and red white board markers in the same hand as he switches back and forth between them.

 

[agrimm2]

There's no simple closed form solution for this unless you all are studying the Lambert W function. Are you?

No i am not, i am basically starting out now with calculus and I was reading a part on how to determine if one kind of function dominates another as they go to infinity. That is where I saw those equations and i got curious to see if there was a way to find an x value where they equal.

 

[agrimm2]

There's also another solution at x ≈ 9.9395351414269

EDIT:You can see this on the far right of @skeeter 's graph - it has a very steep gradient and therefore it almost looks like a border of the image!

Thank you, I saw a similar answer on another site but had no idea how they got it.