SOLUTION: 3^2(x+1) - 8×3^x+1 = 9

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Question 1179352: 3^2(x+1) - 8×3^x+1 = 9
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


The equation you show is 3^2(x+1) - 8*3^x+1 = 9 = 3%5E2%28x%2B1%29+-+8%2A3%5Ex%2B1+=+9

I will assume that is not the equation you wanted.

If you are working problems like this, your mathematical knowledge should be sufficient to know that the proper use of parentheses is important....

I will assume, to make the equation (and therefore the problem) reasonable, that this is the equation you want:

3^(2(x+1)) - 8*3^(x+1) = 9 = 3%5E%282%28x%2B1%29%29+-+8%2A3%5E%28x%2B1%29+=+9

Let u=3%5E%28x%2B1%29
Then note that u%5E2+=+%283%5E%28x%2B1%29%29%5E2+=+3%5E%282%28x%2B1%29%29

Then the equation is

u%5E2-8u=9
u%5E2-8u-9=0
%28u-9%29%28u%2B1%29=0

The two potential solutions are u=9 and u=-1.

(1) u=9
u+=+3%5E%28x%2B1%29+=+9+=+3%5E2
x%2B1=2
x=1

(2) u=-1
u+=+3%5E%28x%2B1%29+=+-1

This value of u provides no real solutions....

ANSWER: there is one solution, x=1.