SOLUTION: 27=3^(5x)*9^(x^2)

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Question 106237: 27=3^(5x)*9^(x^2)
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
27=3%5E%285x%29%2A9%5E%28x%5E2%29
3%5E%285x%29%2A9%5E%28x%5E2%29=27
log%283%5E%285x%29%2A9%5E%28x%5E2%29%29=log%2827%29
log%283%5E%285x%29%29%2Blog%289%28x%5E2%29%29=log%2827%29
5x+log%283%29%2Bx%5E2+log%289%29=log%2827%29
Instead of logarithm of base ten, let's make it base 3 because 3%5E1=3, 3%5E2=9, and 3%5E3=27
Thus,
5x%281%29%2Bx%5E2%282%29=3
5x%2B2x%5E2=3
2x%5E2%2B5x=3
2x%5E2%2B5x-3
Using the quadratic formula,
x=%28-5%2B-sqrt%285%5E2-4%2A2%2A%28-3%29%29%29%2F%282%2A2%29
x=%28-5%2B-sqrt%2825%2B24%29%29%2F%284%29
x=%28-5%2B-sqrt%2849%29%29%2F%284%29
x=%28-5%2B-+7%29%2F%284%29
x=%28-5%2B7%29%2F%284%29 or x=%28-5-7%29%2F%284%29
x=2%2F4 or x=-12%2F4
x=1%2F2 or x=-3

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