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Thread: help with natural logs and logs based of 10

  1. #1
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    help with natural logs and logs based of 10

    My teacher told the tutors at my school not to help us on are homework and I don't have enough money to get a tutor
    so this is my only hope. help with natural logs and logs based of 10-1st-log.jpg I don't how to start on this.
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  2. #2
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    Re: help with natural logs and logs based of 10

    $e^x-6e^{-x}-1=0$

    Multiply every term by $e^x$ ...

    $e^{2x}-6-e^x=0$

    $e^{2x}-e^x-6=0$

    let $u=e^x$ and solve the resulting factorable quadratic equation.

    Got you started ... finish it.
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    Re: help with natural logs and logs based of 10

    Ihelp with natural logs and logs based of 10-log-1st-check.jpg think I got it right
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    Re: help with natural logs and logs based of 10

    Quote Originally Posted by dtdj13 View Post
    IClick image for larger version. 

Name:	Log 1st check.jpg 
Views:	3 
Size:	945.9 KB 
ID:	37359 think I got it right
    uh, no ... you didn't.
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    Re: help with natural logs and logs based of 10

    $\left| \begin{array}{l}e^{2x}-e^x-6=0\\(e^x-3)(e^x+2)=0\\e^x=3~~\&~~e^x=-2\end{array} \right.$

    But it is impossible for $e^x$ to be negative, so there is but one answer: $x=\log(3)$.
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