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Math Help - Writing an expression in fraction form

  1. #1
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    Writing an expression in fraction form

    I have the expressions for the nth term of various sequences. I'm supposed to write them in a "p/q" fraction form, but i have no idea how to do this with logarithmic expressions.

    log2^n(8)
    log3^n(81)
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  2. #2
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    Quote Originally Posted by organismal View Post
    I have the expressions for the nth term of various sequences. I'm supposed to write them in a "p/q" fraction form, but i have no idea how to do this with logarithmic expressions.

    log2^n(8)
    log3^n(81)

    If, for example , you meant \log_{2^n}8=\frac{3}{n} , and this follows at once from the very definition of logarithms. Check it and understand it.

    Tonio
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  3. #3
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    i'm sorry if im misunderstanding what you're saying, but it's not an equation..?

    i was given a sequence:

    <br />
\log_{2}8, \log_{4}8, \log_{8}8, \log_{16}8, \log_{32}8<br />

    i was supposed to write down the next two terms:

    <br />
\log_{64}8, \log_{128}8<br />

    and find an expression fo the nth term of each sequence

    <br /> <br />
\log_{2^n}8<br />

    which i am hoping is correct. then it says to write your expression in the form p/q, meaning a fraction (or I suppose a whole number if it works out that way).

    i tried writing it in exponental form and got to (2^n)^x=8 but that doesn't make any sense to me

    edit: nevermind, i'm sorry, i think i just understood what it was was asking for and your explanation. thank you very much!
    Last edited by organismal; February 15th 2010 at 08:04 PM.
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  4. #4
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    Quote Originally Posted by organismal View Post
    i'm sorry if im misunderstanding what you're saying, but it's not an equation..?

    i was given a sequence:

    <br />
\log_{2}8, \log_{4}8, \log_{8}8, \log_{16}8, \log_{32}8<br />

    i was supposed to write down the next two terms:

    <br />
\log_{64}8, \log_{128}8<br />

    and find an expression fo the nth term of each sequence

    <br /> <br />
\log_{2^n}8<br />

    which i am hoping is correct. then it says to write your expression in the form p/q, meaning a fraction (or I suppose a whole number if it works out that way).

    i tried writing it in exponental form and got to (2^n)^x=8 but that doesn't make any sense to me
    \log_2{8} = \log_{2^1}{8} = \log_{2^1}{(2^1)^\frac{3}{1}} = \frac{3}{1}

    \log_4{8} = \log_{2^2}{8} = \log_{2^2}{(2^2)^{\frac{3}{2}}} = \frac{3}{2}

    \log_8{8} = \log_{2^3}{8} = \log_{2^3}{(2^3)^{\frac{3}{3}}} = \frac{3}{3}

    \log_8{8} = \log_{2^4}{8} = \log_{2^4}{(2^4)^{\frac{3}{4}}} = \frac{3}{4}

    \log_{16}{8} = \log_{2^5}{8} = \log_{2^5}{(2^5)^{\frac{3}{5}}} = \frac{3}{5}.


    I think you can see that:

    \log_{2^n}{8} = \frac{3}{n}.
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