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# How to solve equations?

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How to solve this equation?

Dec 2, 2017

#1
+8061
+1

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!

Dec 2, 2017
edited by asinus  Dec 2, 2017
edited by asinus  Dec 2, 2017
#2
+27540
+3

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

.

Dec 2, 2017
#3
+17286
+2

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

Dec 2, 2017
#4
+1368
+1

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.

GA

GingerAle  Dec 2, 2017
edited by GingerAle  Dec 2, 2017
#5
+99282
+1

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