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Solve 2^x = x^2.

 Oct 27, 2019
 #1
avatar+109202 
+2

2^x  = x^2          take the log of each side

 

log 2^x  = log x^2      and we can write

 

x log 2  =  2 log x

 

Rearrange as

 

 

x / log x   =  2 / log 2

 

And it must be that  x   =   2

 

 

 

cool cool cool

 Oct 27, 2019
 #4
avatar+683 
+1

i'm not the person that asked this question, but i have a question....
i have been wondering abt this for a long time... 

wouldn't it also work with natural logs?

Nirvana  Oct 28, 2019
 #5
avatar+109202 
+1

Yep...we could use the natural log.....but.....apparently......the "log" approach  won't provide all the solutions....

 

 

 

cool cool cool

CPhill  Oct 28, 2019
edited by CPhill  Oct 28, 2019
 #6
avatar+683 
0

ah i see :D 

thanks for clarifying CPhill! 

Nirvana  Oct 29, 2019
 #2
avatar+313 
+3

Apparently 4 is a possible solution as well, according to WolframAlpha. However, I have no idea how to solve it.

 Oct 27, 2019
 #3
avatar+109202 
+2

Yes....you are correct   !!!!

 

I missed that

 

Maybe  this graph will  help  :  https://www.desmos.com/calculator/wisoaf84zp

 

 

 

cool cool cool

CPhill  Oct 27, 2019

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