SOLUTION: Solve the exponential equation. 3^(x^2+5x) = 1/81

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Question 373563: Solve the exponential equation.

3^(x^2+5x) = 1/81
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Note that 1%2F81+=+1%2F%283%5E4%29
1%2F%283%5E4%29+=+3%5E%28-4%29
So, now I can write
3%5E%28x%5E2+%2B+5x%29+=+3%28-4%29
x%5E2+%2B+5x+=+-4
Solve by completing square
x%5E2+%2B+5x+%2B+%285%2F2%29%5E2+=+-4+%2B+%285%2F2%29%5E2
%28x+%2B+5%2F2%29%5E2+=+25%2F4+-+16%2F4
%28x+%2B+5%2F2%29%5E2+=+%283%2F2%29%5E2
x+%2B+5%2F2+=+3%2F2
x+=+-+1
and also
x+%2B+5%2F2+=+-3%2F2
x+=+-4
check the answers:
3%5E%28x%5E2%2B5x%29+=+1%2F81
3%5E%281+%2B+5%2A%28-1%29%29+=+1%2F81
3%5E%28-4%29+=+3%5E%28-4%29
OK
and also
3%5E%28%28-4%29%5E2+%2B+5%2A%28-4%29%29+=+1%2F81
3%5E%2816+-+20%29+=+3%5E%28-4%29
3%5E%28-4%29+=+3%5E%28-4%29
OK