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Solve the equation `(e^x*e^(2x))/e^(x - 1) = 1` . What are the rules to be used.

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lxsptter | Student, Undergraduate

Posted May 6, 2013 at 2:36 AM via web

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Solve the equation `(e^x*e^(2x))/e^(x - 1) = 1` . What are the rules to be used.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 6, 2013 at 2:41 AM (Answer #1)

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The equation `(e^x*e^(2x))/e^(x - 1) = 1` has to be solved.

Use the following rules: `x^a*x^b = x^(a+b)` , `x^a/x^b = x^(a-b)` and `x^0 = 1` .

`(e^x*e^(2x))/e^(x - 1) = 1`

=> `e^(x + 2x - (x - 1)) = 1`

=> `e^(x + 2x - x + 1) = 1`

=> `e^(2x + 1) = 1`

=> `e^(2x + 1) = e^0`

As the base is the same the exponent can be equated.

=> 2x + 1 = 0

=> x = `-1/2`

The solution of the equation `(e^x*e^(2x))/e^(x - 1) = 1` is `x = -1/2`

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