+0

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

0
1851
5

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

Guest Jun 3, 2015

#2
+27223
+10

Solutions can be seen more easily from the following:

.

Alan  Jun 3, 2015
#1
+94101
+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
+27223
+10

Solutions can be seen more easily from the following:

.

Alan  Jun 3, 2015
#3
+94101
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
+27223
+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
+94101
0

Thanks Alan, that makes sense :)

Melody  Jun 3, 2015