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Solve each equation for x to the nearest tenth. (3e)^(4x - 6) = 18

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rosey-girl | Student, Grade 12 | Valedictorian

Posted May 6, 2013 at 3:37 AM via web

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Solve each equation for x to the nearest tenth.

(3e)^(4x - 6) = 18

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 6, 2013 at 3:48 AM (Answer #1)

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The equation `(3e)^(4x) - 6 = 18` has to be solved for x.

`(3e)^(4x) - 6 = 18`

=> `(3e)^(4x) = 24`

take the natural log of both the sides

=> `4x*ln(3*e) = ln 24`

=> `4x*(ln 3 + ln e) = ln 24`

=> `4x*(1 + ln 3) = ln 24`

=> `x = (ln 24)/(4*(1+ln 3))`

=> `x ~~ 0.3785`

The solution of the equation is `x ~~ 0.38`

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