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Solve this equation for x to the nearest tenth. `(2e)^(x-3) + 7 = 27`

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rosey-girl | Student, Grade 12 | (Level 1) Valedictorian

Posted May 6, 2013 at 3:57 AM via web

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Solve this equation for x to the nearest tenth.

`(2e)^(x-3) + 7 = 27`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 6, 2013 at 4:05 AM (Answer #1)

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The equation `(2e)^(x-3) + 7 = 27` has to be solved

`(2e)^(x-3) + 7 = 27`

=> `(2e)^(x-3) = 20`

take the natural log of both the sides

`(x - 3)*ln(2*e) = ln 20`

=> `(x - 3)*(ln 2 + ln e) = ln 20`

=> `(x - 3) = (ln 20)/(ln 2 + ln e)`

=> `x = 3 + (ln 20)/(ln 2 + ln e)`

=> `x = 3 + (ln 20)/(ln 2 + 1)`

=> `x ~~ 4.76 `

The solution of the equation is x = 4.8

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