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Math Help - logarithm

  1. #1
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    logarithm

    Hi, can someone help with this

    How do i prove that the following statement is true?
    2^log(5) is equal to 5^log(2)

    Thanks a lot
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by papercut06 View Post
    Hi, can someone help with this

    How do i prove that the following statement is true?
    2^log(5) is equal to 5^log(2)

    Thanks a lot
    let 2^log(5) = x
    take log of both sides, we get:

    log[2^log(5)] = log(x)
    => log(5)*log(2) = log(x) ................since log(a^b) = blog(a)
    => log(2)*log(5) = log(x)
    => log(5)^log(2) = log(x) ................since blog(a) = log(a^b)
    now we can drop the logs, we get
    5^log(2) = x
    but 2^log(5) = x
    => 5^log(2) = 2^log(5)


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  3. #3
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    earboth's Avatar
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    Quote Originally Posted by papercut06 View Post
    Hi, can someone help with this

    How do i prove that the following statement is true?
    2^log(5) is equal to 5^log(2)

    Thanks a lot
    Hello,

    I used a slightly different way than Jhevon. I've attached a screenshot of my calculations:
    Attached Thumbnails Attached Thumbnails logarithm-log_gleich.gif  
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by earboth View Post
    Hello,

    I used a slightly different way than Jhevon. I've attached a screenshot of my calculations:
    that's a nice way earboth, but i don't think you should have that 2^log(5) at the front, the last line should start with the 5^log(2) i believe
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