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Math Help - multiplying logs

  1. #1
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    multiplying logs

    Hi;
    how do you multiply logs ie log[base2](4) * log[base2](16) I think you work out each log seperately then multiply the solution,Is this the correct process?

    Here I get 8.

    Also do I do the same thing with different bases?

    Thanks.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: multiplying logs

    Your answer is correct.

    Just use the definition like you've done.
    \log_a(x)=y \Leftrightarrow a^y=x
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  3. #3
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    Re: multiplying logs

    Ok do I do the same thing with different bases?
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  4. #4
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    Re: multiplying logs

    It depends, for example if you've different bases you can use:
    \log_a(x)\cdot \log_x(y)=\log_a(y)
    For example:
    \log_2(4)\cdot \log_4(16)=\log_2(16)=4

    And offcourse you can use the definition.
    \log_2(4)\cdot \log_4(16)=2\cdot 2=4

    Is this clear?...
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  5. #5
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    Re: multiplying logs

    got to take a break from study back tommorow.

    Thanks.
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: multiplying logs

    You're welcome!
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  7. #7
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    Re: multiplying logs

    No thats not clear.
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  8. #8
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    Re: multiplying logs

    What's not clear? ...
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  9. #9
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    Re: multiplying logs

    Until I know more will the way I did it work for the same and different bases?
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  10. #10
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    Re: multiplying logs

    What you did is fine, but using this log rules can be really useful sometimes. What have you learned yet about logarithms? Only the definition? ...
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  11. #11
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    Re: multiplying logs

    Yeah not much just doing logs now.
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