How to solve this equation? 

Guest Dec 2, 2017

How to solve this equation?

\( {3^{2}}^x+3^x-2=0\)


\({3^{2}}^x+3^x-2=0\\ 3^{(2^x)}+3^x=2\\ 3^{(2^x)}=2-3^x \)

\(2^x\times ln\ 3=ln\ (2-3^x)\)


Excuse me!


asinus  Dec 2, 2017
edited by asinus  Dec 2, 2017
edited by asinus  Dec 2, 2017

This requires a numerical solution method.  Draw a graph first to see where the solution(s) might lie.



Alan  Dec 2, 2017

Agree with asinus....graphical method is easiest....here is my result from desmos calculator:



ElectricPavlov  Dec 2, 2017

Humm ... I might need to slow down on the fermented bananas, I didn’t notice any mention of a graphical method by Asinus. 


The graphical method may be the easiest when you are using a computerized graphing tool that iterates the value of (x) over a range that includes y=0.   

Do it with graphing paper; calculate each plotted point with a calculator (or a slide rule) and then explain how it’s easier.indecision    




GingerAle  Dec 2, 2017
edited by GingerAle  Dec 2, 2017

Hi Ginger,

Graphing it  is easier because than asinus's method becasue asinus never got an answer.

He just re-arranged it a little and then realized that he didn't know how to solve it. 

Melody  Dec 2, 2017

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