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Math Help - a basic logarithms question.

  1. #1
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    a basic logarithms question.

    {25^{log_5 x}} = 5

    The small number right below the log, after it says it...

    what is that and how would i find significance in that?

    I have already converted the problem to look like the following:

    {log_{25}} 5 = log_5 x.

    I am looking to solve for X.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by beli3ve View Post
    {25^{log_5 x}} = 5

    The small number right below the log, after it says it...

    what is that and how would i find significance in that?

    I have already converted the problem to look like the following:

    {log_{25}} 5 = log_5 x.

    I am looking to solve for X.


    25^{ \log_5 x} = 5

    \Rightarrow \left( 5^2 \right)^{ \log_5 x} = 5

    \Rightarrow 5^{ 2 \log_5 x } = 5

    Now equate the powers, we get:

    2 \log_5 x = 1

    can you take it from here?
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  3. #3
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    Quote Originally Posted by Jhevon View Post

    25^{ \log_5 x} = 5

    \Rightarrow \left( 5^2 \right)^{ \log_5 x} = 5

    \Rightarrow 5^{ 2 \log_5 x } = 5

    Now equate the powers, we get:

    2 \log_5 x = 1

    can you take it from here?
    i am unsure.
    from here, i would divide the two to the other side, making it.

     log_5 x = 1/2 .

    that is an option on my paper, but i am still confused to the significance of what the 5 is?
    actually, as I was just sitting here thinking, is that the number it would represent that was sharing the powers?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by beli3ve View Post
    i am unsure.
    from here, i would divide the two to the other side, making it.

     log_5 x = 1/2 .

    that is an option on my paper, but i am still confused to the significance of what the 5 is?
    actually, as I was just sitting here thinking, is that the number it would represent that was sharing the powers?
    again, remember the rule i told you about.

    If \log_a b = c, then a^c = b


    So we have 2 \log_5 x = 1 .....you divided both sides by 2, which is fine, but is not what i would have done

    \Rightarrow \log_5 x = \frac {1}{2}

    \Rightarrow 5^{ \frac {1}{2}} = x .....i applied the law above

    \Rightarrow x = \sqrt {5}
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    again, remember the rule i told you about.

    If \log_a b = c, then a^c = b


    So we have 2 \log_5 x = 1 .....you divided both sides by 2, which is fine, but is not what i would have done

    \Rightarrow \log_5 x = \frac {1}{2}

    \Rightarrow 5^{ \frac {1}{2}} = x .....i applied the law above

    \Rightarrow x = \sqrt {5}
    the

    x = \sqrt {5}

    makes little sense to me because

    x = 5^{1/2} & x = \sqrt {5}

    are not the same thing to me.
    to me, it could only the square root if

    x = 5^{2}
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by beli3ve View Post
    the

    x = \sqrt {5}

    makes little sense to me because

    x = 5^{1/2} & x = \sqrt {5}

    are not the same thing to me.
    to me, it could only the square root if

    x = 5^{2}
    ummm, 5^{ \frac {1}{2}} is \sqrt {5}

    see http://www.mathhelpforum.com/math-he...tial-form.html

    and look at your statement again. you said x = 5^2 means x is the squareroot of 5. that makes no sense. if x = 5^2, it means x is the square of 5, since if we square 5, we get 5^2 which is equal to x
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  7. #7
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    Quote Originally Posted by Jhevon View Post
    ummm, 5^{ \frac {1}{2}} is \sqrt {5}

    see http://www.mathhelpforum.com/math-he...tial-form.html

    and look at your statement again. you said x = 5^2 means x is the squareroot of 5. that makes no sense. if x = 5^2, it means x is the square of 5, since if we square 5, we get 5^2 which is equal to x
    that makes a lot more sense to me now.
    i do see my errors.
    again, thank you.
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by beli3ve View Post
    that makes a lot more sense to me now.
    i do see my errors.
    again, thank you.
    ok. keep practicing
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