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Thread: Solving problems with natural logs

  1. #1
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    Solving problems with natural logs

    $\displaystyle \ln(x^2)=10$

    I know how to solve this by turning it into an exponential form ie.

    $\displaystyle e^{10}=x^2$

    and solving from there but can you do something like this

    $\displaystyle e^{\ln(x^2)}=e^{10}$

    $\displaystyle e^{2\ln(x)}=e^{10}$

    I don't know what to do from here.
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  2. #2
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    Re: Solving problems with natural logs

    If $\displaystyle e^{2\ln(x)}=e^{10}$ You can put their indexes equal to each other so $\displaystyle 2ln(x)=10$
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  3. #3
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    Re: Solving problems with natural logs

    Where would I go from there? Does that get me any closer to solving for x? Sorry if I'm missing what you are getting at.
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  4. #4
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    Re: Solving problems with natural logs

    From $\displaystyle 2ln(x)=10$ you can continue
    $\displaystyle ln(x)=5$
    $\displaystyle x=e^5$

    And you get the same answer as your first method
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  5. #5
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    Re: Solving problems with natural logs

    Ah, I see. Apparently I'm a little rusty at this stuff. Thanks for the help.
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  6. #6
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    Re: Solving problems with natural logs

    You should brush up on your log properties.

    $\displaystyle \log_b{a^n} = n \log_b{a}$ would have saved you time
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