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Math Help - Log comparision question

  1. #1
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    Log comparision question

    "Which is greater, \log_3{5}   or \log_5{11}? Explain"

    Although u can plug and chug into your calculator, this question seems like it's meant to be solved analytically.

    I got to:

    \log_3{5}=a  , \log_5{11}=b
    3^a=5, 5^b=11
    (3^a)^b=11<br />

    Dunno what's next. I can figure out that a<2 and ab>2
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Uncle6 View Post
    "Which is greater, \log_3{5}   or \log_5{11}? Explain"

    Although u can plug and chug into your calculator, this question seems like it's meant to be solved analytically.

    I got to:

    \log_3{5}=a  , \log_5{11}=b
    3^a=5, 5^b=11
    (3^a)^b=11<br />

    Dunno what's next. I can figure out that a<2 and ab>2
    think of it this way:

    we have 3^a = 5 and 5^b = 11

    Note that 5 is less than twice 3, while 11 is more than twice 5. in other words, b has the task of increasing the base 5 a larger magnitude (relatively speaking) than a has to do for 3. b is larger


    this is a more intuitive approach. which i suppose is the level of thinking this problem requires, since it is elementary/middle school math. there are more rigorous proofs, i'm sure
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  3. #3
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    Thanks, but it still is quite difficult to understand.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Uncle6 View Post
    Thanks, but it still is quite difficult to understand.
    where particularly is your difficulty?
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  5. #5
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    in other words, b has the task of increasing the base 5 a larger magnitude (relatively speaking) than a has to do for 3
    I get lost here. Would u know how to write it out as a proof?
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