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6*4^x-13*6^x+6*9^x=0

Guest Jun 3, 2015

Best Answer 

 #2
avatar+26329 
+10

Solutions can be seen more easily from the following:

 

 exponent solutions:

.

Alan  Jun 3, 2015
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5+0 Answers

 #1
avatar+91049 
+10

 

Integer solutions are x = + or - 1

 

http://www.wolframalpha.com/input/?i=6*4%5Ex-13*6%5Ex%2B6*9%5Ex%3D0

Melody  Jun 3, 2015
 #2
avatar+26329 
+10
Best Answer

Solutions can be seen more easily from the following:

 

 exponent solutions:

.

Alan  Jun 3, 2015
 #3
avatar+91049 
0

Thanks Alan

I would not have thought to do that.

How can you tell that there will be another solution as as  $$x\rightarrow -\infty$$   ?

Melody  Jun 3, 2015
 #4
avatar+26329 
+5

Because, if you look at the original form of the equation, 4-∞ = 0, 6-∞ = 0 and 9-∞ = 0 i.e. each of the terms on the LHS is individually zero.

 

In that limit my rearranged version of the equation doesn't hold, because a divide by zero would be involved.

.

Alan  Jun 3, 2015
 #5
avatar+91049 
0

Thanks Alan, that makes sense :)

Melody  Jun 3, 2015

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