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Math Help - Student in need of a little help inverting a logarithmic problem

  1. #1
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    Red face Student in need of a little help inverting a logarithmic problem

    Hi!

    My name is Cleo, I'm 19 years old and I am stuck on this little problem here. If anyone could help me, that would be absolutely wonderful.

    I started with this:

    111 = 17 + (13^(1/x)-1)*((550-17): (420^(1/x)-1))

    and rewrote it to

    533*13^(1/x) = 94*420^(1/x) + 439

    But now I'm a little lost... How do I find my x?

    Thanks in advance for your help!
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  2. #2
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    Re: Student in need of a little help inverting a logarithmic problem

    Quote Originally Posted by cleomauritsz View Post
    Hi!

    My name is Cleo, I'm 19 years old and I am stuck on this little problem here. If anyone could help me, that would be absolutely wonderful.

    I started with this:

    111 = 17 + (13^(1/x)-1)*((550-17): (420^(1/x)-1))

    and rewrote it to

    533*13^(1/x) = 94*420^(1/x) + 439

    But now I'm a little lost... How do I find my x?

    Thanks in advance for your help!
    Goeien avond!

    1. This sign ":" means division, right?

    2. I doubt that you can find a solution in closed form . So use Newton's method to find an approximate result.

    3. I've got x \approx 2.512523062
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    Re: Student in need of a little help inverting a logarithmic problem

    Goedenavond!

    The : stands for division, like you said. The point with this problem is, I have a whole list of different observations and for each set, I need to determine the x. The one above is just an example, that's why I'd like to find out how to do it step-by-step... The original problem is A = (B-C)/(420^(1/x)-1)*D^(1/x)+E-(B-C)/(420^(1/x)-1)
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  4. #4
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    Re: Student in need of a little help inverting a logarithmic problem

    Quote Originally Posted by cleomauritsz View Post
    Goedenavond!

    The : stands for division, like you said. The point with this problem is, I have a whole list of different observations and for each set, I need to determine the x. The one above is just an example, that's why I'd like to find out how to do it step-by-step... The original problem is A = (B-C)/(420^(1/x)-1)*D^(1/x)+E-(B-C)/(420^(1/x)-1)
    In the attachment you find my result of the transformations of the given equation. Certainely you have found these proportions too.

    I'm not able to solve the equation for x en het spijt mij!
    Attached Thumbnails Attached Thumbnails Student in need of a little help inverting a logarithmic problem-loesungsversuch.png  
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