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Math Help - Giving an Exact Solution to a Logarithm

  1. #1
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    Giving an Exact Solution to a Logarithm

    Subject are exactly what the instructions are and I have no problem doing logarithms until I came upon this problem. Teacher didn't really give any examples like this one and I am totally lost.


    I have no idea how to write that exactly as I see it
    Any help is GREATLY appreciated thank you!Giving an Exact Solution to a Logarithm-math-problem.png
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    Re: Giving an Exact Solution to a Logarithm

    \displaystyle \begin{align*} \log_2{\sqrt{3x^2}} &= \frac{3}{2} \\ \sqrt{3x^2} &= 2^{\frac{3}{2}} \end{align*}

    Go from here.
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    Re: Giving an Exact Solution to a Logarithm

    Giving an Exact Solution to a Logarithm-math-prob.png

    Thank you for the reply.
    I tried that earlier and just got stuck again as I've never done a logarithm like this.

    Am I on the right track? If so I have no idea what to do next =(
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    Re: Giving an Exact Solution to a Logarithm

    The answer I got is X is approximately .9428
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    Re: Giving an Exact Solution to a Logarithm

    Quote Originally Posted by Mollers View Post
    The answer I got is X is approximately .9428
    "approximately" isn't exact though is it
    This problem is completely solvable without a calculator. No decimals!
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    Re: Giving an Exact Solution to a Logarithm

    \log_2(\sqrt{3x^2})=\frac{3}{2}

    \frac{1}{2} \log_2(3x^2)=\frac{3}{2}

    \log_2(3x^2)=3

    3x^2=2^3

    \vdots
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    Re: Giving an Exact Solution to a Logarithm

    I'm using the fact that log(sqrty)=1/2logy
    So from your question we get 1/2log3x^2=3/2 log3x^2=3 So 3x^2=2^3 (since log base is 2)
    So x^2=8/3 x=sqrt(8/3) =root8/root3 =2root2/root3
    Multiply top and bottom by root3 Get x=2root6/3
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    Re: Giving an Exact Solution to a Logarithm

    First off thank you all for the help I couldn't get no where near where I am in this problem without you. I am stuck again as I cannot figure out how to write the last part of what Biffboy said..."root8/root3 =2root2/root3 --------> Multiply top and bottom by root3 Get x=2root6/3"

    Giving an Exact Solution to a Logarithm-math-problem.png

    This is where I get stuck.
    Attached Thumbnails Attached Thumbnails Giving an Exact Solution to a Logarithm-math-problem.png  
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    Re: Giving an Exact Solution to a Logarithm

    ignore the bottom thumbnail
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  10. #10
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    Re: Giving an Exact Solution to a Logarithm

    Quote Originally Posted by Mollers View Post
    First off thank you all for the help I couldn't get no where near where I am in this problem without you. I am stuck again as I cannot figure out how to write the last part of what Biffboy said..."root8/root3 =2root2/root3 --------> Multiply top and bottom by root3 Get x=2root6/3"

    Click image for larger version. 

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    This is where I get stuck.
    Here we go:

    3x^2=8

    x^2=\frac{8}{3}

    x=\sqrt{\frac{8}{3}}

    x=\frac{\sqrt{8}}{\sqrt{3}}

    x=\frac{2\sqrt{2}}{\sqrt{3}}

    "Rationalize" the denominator by multipling numerator and denominator by \sqrt{3}

    x=\frac{2\sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{6}}{3}
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    Re: Giving an Exact Solution to a Logarithm

    thank you so much! I dont understand why I was given this problem when I was never given an example that was anywhere near similar.
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    Re: Giving an Exact Solution to a Logarithm

    I have been looking at this problem more and thinking about it and wanted to make sure about something.

    Since the directions are to give an exact solution would I leave the answer as 2 sqaure root 6/3 or should I compute this and get a decimal answer?
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  13. #13
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    Re: Giving an Exact Solution to a Logarithm

    Leave it as it is. Any decimal answer you got would be an approximation.
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