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Math Help - Logarithms as Inverses.

  1. #1
    Newbie north1224's Avatar
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    Question Logarithms as Inverses.

    Please solve with work and explain why and what you are doing

    Write the Inverse of each function:

    1) Y= log3X

    2) Y= 2^(x/3)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by north1224 View Post
    Please solve with work and explain why and what you are doing

    Write the Inverse of each function:

    1) Y= log3X

    2) Y= 2^(x/3)
    the definition of the logarithm should help you.

    note that \log_a b = c \Longleftrightarrow a^c = b
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by north1224 View Post
    Please solve with work and explain why and what you are doing

    Write the Inverse of each function:

    1) Y= log3X

    2) Y= 2^(x/3)

    y=log_{3}(x)

    exchange the x and y and then solve for y

    x=log_{3}(y) \iff 3^x=y

    f^{-1}(x)=3^x

    y=2^{x/3} swapping the var


    x=2^{y/3} \iff log_{2}(x)=\frac{y}{3} \iff 3log_{2}(x)=y

    f^{-1}(x)=3log_2(x)
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  4. #4
    Newbie north1224's Avatar
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    <br />
y=2^{x/3}<br />
swapping the var

    <br />
x=2^{y/3} \iff log_{2}(x)=\frac{y}{3} \iff 3log_{2}(x)=y<br />
    Where did the 2 come from?
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by north1224 View Post
    Where did the 2 come from?
    the 2 was in the original question. it ended up as the base of the logarithm based on the rule i gave you earlier
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  6. #6
    Newbie north1224's Avatar
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    Quote Originally Posted by Jhevon View Post
    the 2 was in the original question. it ended up as the base of the logarithm based on the rule i gave you earlier
    I Meant the two from "TheEmptySet" description, Thanks anyway, The rule helped me alot for the rest of my worksheet though, thanks for that
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  7. #7
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    It is the rule that Jhevon mentioned above.
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  8. #8
    Newbie north1224's Avatar
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    Quote Originally Posted by TheEmptySet View Post
    It is the rule that Jhevon mentioned above.
    No, TheEmptySet, Where did the 2 as a variable come from.?
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  9. #9
    Behold, the power of SARDINES!
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    Quote Originally Posted by north1224 View Post
    No, TheEmptySet, Where did the 2 as a variable come from.?
    I don't understand 2 is a constant not a variable?

    your equation is

    y=2^{\frac{x}{3}}

    The 2 is the base of eponential function.

    if we interchange the variables we get

    x=2^{\frac{y}{3}} rewritting as a log we get

    log_{2}(x)=\frac{y}{3} \iff y= 3 log_{2}(x)
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  10. #10
    Newbie north1224's Avatar
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    My Bad

    Quote Originally Posted by TheEmptySet View Post
    I don't understand 2 is a constant not a variable?

    your equation is

    y=2^{\frac{x}{3}}

    The 2 is the base of eponential function.

    if we interchange the variables we get

    x=2^{\frac{y}{3}} rewritting as a log we get

    log_{2}(x)=\frac{y}{3} \iff y= 3 log_{2}(x)
    My Bad dude. I was thinking that you were only doing #1 i didnt realize you were doing both. I was trying to figure out how you got a two into the first question. LOL
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