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What is solution of equation (e^3x+3)(e^3x-1)=0?

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greynose | Student, Undergraduate | Honors

Posted August 10, 2011 at 10:17 PM via web

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What is solution of equation (e^3x+3)(e^3x-1)=0?

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giorgiana1976 | College Teacher | Valedictorian

Posted August 10, 2011 at 10:22 PM (Answer #1)

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We notice that the given equation is a product of two factors. This product is zero if one of the factors is zero.

We'll cancel each factor:

`e^(3x)` + 3 = 0

`e^(3x)` = -3

There is no such value of x for `e^(3x)` to give a negative value, therefore `e^(3x)` + 3 > 0, but never 0.

We'll cancel the next factor:

`e^(3x)` - 1 = 0

`e^(3x)` = 1

We'll create matching bases both sides:

`e^(3x)` = `e^(0)`

Since the bases are matching, we'll equate the exponents:

3x = 0

x = 0

The solution of the equation is x = 0.

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