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Solve the equation 3^(3x^2+5x-4)=9^-3

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portoruj | Student, Grade 10 | eNoter

Posted May 24, 2011 at 7:24 AM via web

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Solve the equation

 3^(3x^2+5x-4)=9^-3

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giorgiana1976 | College Teacher | Valedictorian

Posted May 24, 2011 at 9:44 PM (Answer #2)

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Writing 9 as a power of 3, we'll create matching bases both sides: 9 = 3^2

We'll apply the rule of negative power:

a^-b = 1/a^b

We'll put a = 9 and b = -3

9^-3 = 1/9^3 = 1/(3^2)^3 = 1/3^6 = 3^-6

We'll re-write the equation:

3^(3x^2 + 5x - 4) = 3^-6

Since the bases are matching, we'll apply one to one rule and we'llequate superscripts:

3x^2 + 5x - 4 = -6

3x^2 + 5x - 4+6 = 0

3x^2 + 5x + 2 = 0

We'll apply the quadratic formula:

x1 = [-5+sqrt(25 - 24)]/6

x1 = (-5+1)/6

x1 = -2/3

x2 = -1

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