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Math Help - quick log question...

  1. #1
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    quick log question...

    Simplify 2loga+3logb:

    I thought it you could do add the 2 and 3, but multiply a + b to give 5logab.

    But the answer says: 2loga+3logb = log{a^2}+log{b^2} = log{a^2}{b^3}.

    I perfectly understand how the mark scheme did it, moving the powers of 2 and 3 form the log laws, but i was just wondering though:

    Is it wrong adding the first bit I did of the 2 and the 3 before the logs, and multiplying the a and b?

    Thanks.
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  2. #2
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    Quote Originally Posted by chinkmeista View Post
    Simplify 2loga+3logb:

    I thought it you could do add the 2 and 3, but multiply a + b to give 5logab.

    But the answer says: 2loga+3logb = log{a^2}+log{b^2} = log{a^2}{b^3}.

    I perfectly understand how the mark scheme did it, moving the powers of 2 and 3 form the log laws, but i was just wondering though:

    Is it wrong adding the first bit I did of the 2 and the 3 before the logs, and multiplying the a and b?

    Thanks.
    Use the law klog(a) = log(a^k)

    then you can use the law log(a) + log(b) = log(ab)
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  3. #3
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    Quote Originally Posted by e^(i*pi) View Post
    Use the law klog(a) = log(a^k)

    then you can use the law log(a) + log(b) = log(ab)
    Oh ok, you can only do  log(a) + log(b) = log(ab) after that power rule?

    If the question was 2log(a)+3log(a),can i add it then to 5log(a^2) because they're both 'a' or do i still have to use that power rule first and make it log(a^2) + log(a^3) = log(a^5)?
    Last edited by mr fantastic; May 21st 2009 at 03:27 AM. Reason: Fixed latex
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by chinkmeista View Post
    Oh ok, you can only do log(a) + log(b) = log(ab) after that power rule?

    If the question was 2log(a)+3log(a),can i add it then to 5log(a^2) because they're both 'a' or do i still have to use that power rule first and make it log(a^2) + log(a^3) = log(a^5)?
    You have to use the power law in your first example because your logs are not the same because 2 does not equal 3.

    In your second example you can add them because a=a. Think about what happens if you use the power rule on log(a^5)
    Last edited by mr fantastic; May 21st 2009 at 03:28 AM.
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  5. #5
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    Quote Originally Posted by e^(i*pi) View Post
    You have to use the power law in your first example because your logs are not the same because 2 does not equal 3.

    In your second example you can add them because a=a. Think about what happens if you use the power rule on log(a^5)
    nice one, cheers buddy lol, ive actually spent a hour on this minor problem! lol thanks.
    Last edited by mr fantastic; May 21st 2009 at 03:26 AM.
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