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3 - 4ln(8x+1) = 12

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user6968207 | Student | eNotes Newbie

Posted May 2, 2013 at 10:12 PM via web

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3 - 4ln(8x+1) = 12

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oldnick | (Level 1) Valedictorian

Posted May 2, 2013 at 10:53 PM (Answer #1)

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`3-4log(8x+1)=12`

`-4log(8x+1)=9`

`log(8x+1)=-9/4`

`8x+1=e^(-9/4)`

`x=(e^(-9/4)-1)/8`

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mjripalda | High School Teacher | (Level 1) Senior Educator

Posted May 2, 2013 at 11:41 PM (Answer #2)

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`3 - 4ln(8x+1) = 12`

To isolate the x, first subtract both sides by 3.

`3-3 - 4ln(8x+1) = 12-3`

`-4ln(8x+1)=9`

Then, divide both sides by -4.

`(-4ln(8x+1))/(-4)=9/(-4)`

`ln(8x+1)=-9/4`

From here, convert this to exponential equation.

Note that the equivalent exponential form of a logarithmic equation `ln M= a`  is  `M=e^a` .

`8x+1=e^(-9/4)`

Then, subtract both sides by 1.

`8x+1-1=e^(-9/4) - 1`

`8x=e^(-9/4)-1`

And divide both sides by 8.

`(8x)/8=(e^(-9/4)-1)/8`

`x=(e^(-9/4)-1)/8`

Hence, the solution to the given equation is `x=(e^(-9/4)-1)/8` .

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