SOLUTION: {{{8 = 4^(x^2)*2^(5x)}}} Solve for x.

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Question 972085: 8+=+4%5E%28x%5E2%29%2A2%5E%285x%29 Solve for x.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
8+=+4%5E%28x%5E2%29%2A2%5E%285x%29

2%5E3=%282%5E2%29%5E%28x%5E2%29%2A2%5E%285x%29

2%5E3=%282%5E%282x%5E2%29%29%2A2%5E%285x%29

2%5E3=2%5E%282x%5E2%2B5x%29


Same base of 2 on both sides, so their exponents are equal:

3=2x%5E2%2B5x------More easily solvable in this form now.



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You should at least obtain a quadratic equation equivalent to the one shown there.

2x%5E2%2B5x-3=0
discriminant is 25%2B8%2A3=25%2B24=49=7%5E2.
The quadratic part is factorable.(?)
x=%28-5%2B-+7%29%2F4
x=-3 or x=1/2

or,
%282x-1%29%28x%2B3%29=0