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# help

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Solve 2^x = x^2.

Oct 27, 2019

#1
+109202
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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

Oct 27, 2019
#4
+683
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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
+109202
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Yep...we could use the natural log.....but.....apparently......the "log" approach  won't provide all the solutions....

CPhill  Oct 28, 2019
edited by CPhill  Oct 28, 2019
#6
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ah i see :D

thanks for clarifying CPhill!

Nirvana  Oct 29, 2019
#2
+313
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Apparently 4 is a possible solution as well, according to WolframAlpha. However, I have no idea how to solve it.

Oct 27, 2019
#3
+109202
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Yes....you are correct   !!!!

I missed that

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

CPhill  Oct 27, 2019