SOLUTION: solve 25^y + 3 (5^y) =3

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Question 1062497: solve 25^y + 3 (5^y) =3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
25^y + 3 (5^y) =3
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5%5E%282y%29+%2B+3%2A%285%5Ey%29+-+3+=+0
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Sub x for 5^y
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x%5E2+%2B+3x+-+3+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A1%2A-3=21.

Discriminant d=21 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+21+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+21+%29%29%2F2%5C1+=+0.79128784747792
x%5B2%5D+=+%28-%283%29-sqrt%28+21+%29%29%2F2%5C1+=+-3.79128784747792

Quadratic expression 1x%5E2%2B3x%2B-3 can be factored:
1x%5E2%2B3x%2B-3+=+%28x-0.79128784747792%29%2A%28x--3.79128784747792%29
Again, the answer is: 0.79128784747792, -3.79128784747792. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-3+%29

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Ignore the negative value
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x =~ 0.79129
5^y = 0.79129
y*log(5) = log(0.79129)
y = log(0.79129)/log(5)
y =~ -0.14545