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Math Help - combining/simplifying logs (part 2)

  1. #1
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    combining/simplifying logs (part 2)



    Here is the 2nd one which asks to simplify the whole thing as a logarithm. Again, not sure how to take the integers at the end and convert them into log form. Thanks.
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  2. #2
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    Quote Originally Posted by Evan.Kimia View Post


    Here is the 2nd one which asks to simplify the whole thing as a logarithm. Again, not sure how to take the integers at the end and convert them into log form. Thanks.
    3 = log_4 (4^3)

    edit:

    before that I would change 2log_2(8) = 2log_2(2^3) = 6.

    Simplify the two integers and then make that into a log with base 4 to match that of x and y
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  3. #3
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    Thank you, but im a bit confused how to go about changing the base, or if i even have to to log base 4.

    ps., the correct answer is log base 4 (xy^2 over 64)
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    We know that log_a(a) = 1

    Note that 2log_2(8) = 6 because  8=2^3

    2log_4(y) = log_4(y^2)

    -6+3 = -3

    As -3 = log_4(4^{-3}) (see the rule above)

    So overall we can rewrite it as log_4(x)+log_4(y^2)+log_4 \left(\frac{1}{64}\right)

    You can then combine the logs to give:

    log_4 \left(\frac{xy^2}{64}\right)
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  5. #5
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    ah! thank you!
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