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Natural Logarithmic Eqaution `ln x - ln (x-5) = 4`

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rosey-girl | Student, Grade 12 | Valedictorian

Posted April 24, 2013 at 6:17 AM via web

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Natural Logarithmic Eqaution

`ln x - ln (x-5) = 4`

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted April 24, 2013 at 6:38 AM (Answer #1)

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`ln x-ln(x-5)=4`

Now we use the following property of logarithms:

`log_b x-log_b y=log_b x/y`

Hence, we get

`ln(x/(x-5))=4`

`x/(x-5)=e^4`

`x=e^4x-5e^4`

`x-e^4x=-5e^4`

`x(1-e^4)=-5e^4`

`x=-(5e^4)/(1-e^4)`   <-- Your solution

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