SOLUTION: Please solve for x: 3^(2x)-10*3^x+9=0

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Question 141816: Please solve for x:
3^(2x)-10*3^x+9=0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
3%5E%282x%29+-10%2A3%5Ex%2B9+=+0
Try this:
Temporarily change variables by letting:
z+=+3%5Ex and z%5E2+=+%283%5Ex%29%5E2 Make the appropriate substitutions:
z%5E2-10z%2B9+=+0 Factor:
%28z-1%29%28z-9%29+=+0 Apply the zero product rule:
z-1+=+0 or z-9+=+0 so that...
z+=+1 or z+=+9 Now exchange z for z+=+3%5Ex
3%5Ex+=+1 or 3%5Ex+=+9
Make the following substitutions:
1+=+3%5E0 and 9+=+3%5E2
3%5Ex+=+3%5E0 or 3%5Ex+=+3%5E2 Now, if M%5Ea+=+M%5Eb then a+=+b, so...
3%5Ex+=+3%5E0 means that x+=+0
3%5Ex+=+3%5E2 means that x+=+2
Solutions:
x = 0
x = 2
Check:
3%5E%282x%29-10%2A3%5Ex%2B9+=+0 Substitute x = 0
3%5E%282%2A0%29-10%2A3%5E0%2B9+=+0 Simplify.
1-10%281%29%2B9+=+0
1-10%2B9+=+0
0+=+0 OK!
3%5E%282x%29-10%2A3%5Ex%2B9+=+0 Substitute x = 2
3%5E%282%2A2%29-10%2A3%5E2%2B9+=+0 Simplify:
3%5E4-10%2A9%2B9+=+0
81-90%2B9+=+0
81%2B9-90+=+0
0+=+0 OK!