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Solve the exponential equation: `e^(6x^2-1)=13`

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jgoodnig | Student, College Freshman | eNoter

Posted February 8, 2012 at 1:45 AM via web

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Solve the exponential equation: `e^(6x^2-1)=13`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 8, 2012 at 1:52 AM (Answer #1)

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The equation `e^(6x^2 - 1) = 13` has to be solved.

Take the natural log of both the sides.

`6x^2 - 1 = ln 13`

=> `6x^2 = 1 + ln 13`

=> 6x^2 = ln(13 + e)

=> `x^2 = (ln(13 + e))/6`

=> `x^2 = ln(13 + e)^(1/6)`

=> `x = sqrt(ln(13 + e)^(1/6))` and x = `-sqrt(ln(13 + e)^(1/6))`

The solution of the equation is x = `sqrt(ln(13 + e)^(1/6))` and x = ` -sqrt(ln(13 + e)^(1/6))`

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