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Thread: stuck on Logarithmic equation

  1. #1
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    stuck on Logarithmic equation

    Im stuck on this one. I can't figure out the next step. if I devide through by x it gets confusing. could someone show a next step.

    thanks.

    $\displaystyle
    \ln \left( x+2 \right) =1+\ln \left( x \right)
    $

    i get to here...

    $\displaystyle
    {\frac {x+2}{x}}={{\rm e}}
    $

    this is the solution in the book.

    $\displaystyle
    x={\frac {2}{\rm e-1}}
    $
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  2. #2
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    Quote Originally Posted by skoker View Post
    Im stuck on this one. I can't figure out the next step. if I devide through by x it gets confusing. could someone show a next step.

    thanks.

    $\displaystyle
    \ln \left( x+2 \right) =1+\ln \left( x \right)
    $

    i get to here...

    $\displaystyle
    {\frac {x+2}{x}}={{\rm e}}
    $

    this is the solution in the book.

    $\displaystyle
    x={\frac {2}{\rm e-1}}
    $
    Dear skoker,

    Subject x in your equation. For that first you need to multiply both sides by x.
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  3. #3
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    ok i think i got it. i have to factor out x.

    $\displaystyle
    x+2={{\rm e}}x
    $

    $\displaystyle
    2=x \left \left( e-1 \right)
    $

    $\displaystyle
    x={\frac {2}{\rm e-1}}
    $


    thanks.
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  4. #4
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    An alternative:

    $\displaystyle \displaystyle \frac{x + 2}{x} = e$

    $\displaystyle \displaystyle 1 + \frac{2}{x} = e$

    $\displaystyle \displaystyle \frac{2}{x} = e-1$

    $\displaystyle \displaystyle \frac{x}{2} = \frac{1}{e-1}$

    $\displaystyle \displaystyle x = \frac{2}{e-1}$.
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  5. #5
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    ah. thats good you posted that. I was trying to figure a way to do it without multiplying through with x. I did not think of flipping both sides like that. interesting.
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  6. #6
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    Here's how I would solve it:

    stuck on Logarithmic equation-ln-x-2-1-ln-x-.pdf
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