Crazy Exponential Equation

I also found this exponential equation on You Tube.

Solve for x.

x^2 = 2^(x)

What would you do?

Is it right to take the natural log on both sides?

ln(x^2) = ln(2^x)

2lnx = x•ln2

If this is the correct first couple of steps, where do we go from here?

NOTE: I can watch the entire video and learn how it is done. I'd rather try to solve it on my own without the video clip. It's more fun this way.

 

so far correct .....good luck

 

Ita "good luck" Wednesday.

 

There is not going to be any "elementary" way to solve this. You should be able to convert into a form where you can use "Lambert's W function" which is defined as the inverse function to f(x)= xe^x.

 

When I realized that the problem is beyond my level of study, I gave up. It looks interesting but I gave up. Sorry.