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Solve equation for x: a) `ln(x^2-1)=3` 

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calculatoror | (Level 1) eNoter

Posted September 23, 2012 at 7:03 PM via web

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Solve equation for x:

a) `ln(x^2-1)=3` 

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lfryerda | High School Teacher | (Level 2) Educator

Posted September 23, 2012 at 8:56 PM (Answer #1)

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If you have more than one question you need to make separate posts.

To solve this equation, we need to change the equation from logarithmic to exponential form.
`ln(x^2-1)=3`   
`x^2-1=e^3`   move 1 to other side
`x^2=1+e^3`   take square roots
`x=+-sqrt{1+e^3}`
For both potential solutions, when we substitute back into the original equation, we get valid solutions.
The solutions of the equation are `x=+-sqrt{1+e^3}` .

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