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Math Help - Log Equation

  1. #1
    Junior Member
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    Log Equation

    <br />
\ln x + \ln (x+2) = 4<br />

    The answer is:
    <br />
x = -1 + \sqrt{1 + e^4}<br />

    so far I've done:

    <br />
log_e x + log_e (x+2) = e^4<br />

    <br />
log_e x^2+2x = e^4<br />

    Stuck.
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  2. #2
    Super Member
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    Quote Originally Posted by desiderius1 View Post
    <br />
\ln x + \ln (x+2) = 4<br />

    The answer is:
    <br />
x = -1 + \sqrt{1 + e^4}<br />

    so far I've done:

    <br />
log_e x + log_e (x+2) = e^4<br />
No it's not

    <br />
log_e x^2+2x = e^4<br />
In the future please put brackets around x^2 + 2x

    Stuck.

     \ln x + \ln (x+2) = 4

     \ln | x(x+2)| = 4

     x^2 + 2x = e^4

     (x+1)^2 = e^4 + 1

     x+1 = \sqrt {e^4 + 1}

     x = -1 + \sqrt{1+e^4}
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  3. #3
    MHF Contributor

    Joined
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    Quote Originally Posted by desiderius1 View Post
    <br />
\ln x + \ln (x+2) = 4<br />

    The answer is:
    <br />
x = -1 + \sqrt{1 + e^4}<br />

    so far I've done:

    <br />
log_e x + log_e (x+2) = e^4<br />
    That's NOT your orignal equation!

    <br />
log_e x^2+2x = e^4<br />

    Stuck.
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