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Math Help - Solve this Logarithm

  1. #1
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    Solve this Logarithm

    3ln(x) - 2ln(y) = 4

    Express y in terms of x

    i think that next it would become

    ln (x)^3 - ln(y)^2 = 4

    But I really am not sure what to do, so if someone could help me out please, that would be great
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  2. #2
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    Start by getting all your \displaystyle x terms on one side and \displaystyle y terms on the other.

    \displaystyle 2\ln{y} = 3\ln{x} - 4.

    Can you go from here?
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  3. #3
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    Quote Originally Posted by Prove It View Post
    Start by getting all your \displaystyle x terms on one side and \displaystyle y terms on the other.

    \displaystyle 2\ln{y} = 3\ln{x} - 4.

    Can you go from here?
    ln(y)^2 = ln(x)^3 -4

    in know that you can eliminate ln, however I'm not sure what to do with the subtraction of 4 on the end
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  4. #4
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    Quote Originally Posted by gbooker View Post
    ln(y)^2 = ln(x)^3 -4

    in know that you can eliminate ln, however I'm not sure what to do with the subtraction of 4 on the end
    You don't need to use this logarithm rule...

    Just remember that the opposite of multiplying by 2 is dividing by 2, and the opposite of a logarithm is an exponential.
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  5. #5
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    Quote Originally Posted by Prove It View Post
    You don't need to use this logarithm rule...

    Just remember that the opposite of multiplying by 2 is dividing by 2, and the opposite of a logarithm is an exponential.
    I must be having a really bad mental blank or something I just can't figure it out
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  6. #6
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    Quote Originally Posted by gbooker View Post
    3ln(x) - 2ln(y) = 4, Express y in terms of x
    You can write it as \ln\left(\frac{x^3}{y^2}\right)=4.

    Recall that \ln(a)=b can be written as a=e^b.
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