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Math Help - [SOLVED] logs

  1. #1
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    [SOLVED] logs

    Does anyone understand these two problems:

    Problem 1:
    (hint: )


    Problem 2:




    help please?

    for 1, I got -2k

    & for 2, I got 3

    which were wrong
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by lsnyder View Post
    Does anyone understand these two problems:

    Problem 1:
    (hint: )
    Incorporating the hint, this is equivalent to:

    \log_{1048576}\left[\left(\left[1048576^{\frac{1}{10}}\right]^{-2}\right)^k\right]=\log_{1048576}\left[\left(1048576\right)^{-\frac{2k}{10}}\right] =-\frac{k}{5}\log_{1048576}\left(1048576\right)=\col  or{red}\boxed{-\frac{k}{5}}


    Problem 2:




    help please?

    for 1, I got -2k

    & for 2, I got 3

    which were wrong
    Note that 3^{6\log_3 5-5\log_3 6}=3^{6\log_3 5}3^{-5\log_3 6}=3^{\log_3\left(5^6\right)}3^{\log_3\left(6^{-5}\right)}

    Can you finish the simplification?

    Does this make sense?
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  3. #3
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    okay i somewhat ubderstand 1.
    i just don't understand where u got 1/10.
    other than that i get it.

    & on problem 2,
    i am very lost.
    where did the 3 come from in between 5 and -5
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  4. #4
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    oh nevermind, i figured out the 1/10 in the 1st problem

    but i still don't follow the second one
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by lsnyder View Post
    okay i somewhat ubderstand 1.
    i just don't understand where u got 1/10.
    other than that i get it.
    In the hint, 1048576=4^{10}\implies 1048576^{\frac{1}{10}}=4. Thus, in your expression, I substituted 1048576^{\frac{1}{10}} for 4.

    Does this clarify things?

    & on problem 2,
    i am very lost.
    where did the 3 come from in between 5 and -5
    I applied rules of exponents:

    a^{b-c}=a^ba^{-c}
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  6. #6
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    yea i got the 1/10 after i posted i didn't understand.
    but problem 1 i understand.

    now on problem 2,
    i see what you did with the 3.
    i have 1 question though.
    Will all the threes cancel out?
    or is there something else i am missing?
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  7. #7
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    nevermind i got problem 2

    if any1 cares the answer was:

    15625/7776
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