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Math Help - Fractal Geometry - logarithms problem

  1. #1
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    Fractal Geometry - logarithms problem

    Hi everyone,

    I have my Fractal exam on Tuesday so I'm getting a bit worried! My problem isn't really about the geometry itself, just a basic log problem that I probably should have learnt years ago....

    Problem Background:
    Finding the Hausdorff dimension of an iterated function system, after composing mappings, I end up with an expression which needs to be solved using logs.

    Problem:

    Solve the equation 2*(1/9)^s+ 2*(1/4)^s = 1 for s.

    In this example, the solution sheet gives s = 0.802, but I have no idea how to get to that. Any help much appreciated!
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  2. #2
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    Quote Originally Posted by rory View Post
    Hi everyone,

    I have my Fractal exam on Tuesday so I'm getting a bit worried! My problem isn't really about the geometry itself, just a basic log problem that I probably should have learnt years ago....

    Problem Background:
    Finding the Hausdorff dimension of an iterated function system, after composing mappings, I end up with an expression which needs to be solved using logs.

    Problem:

    Solve the equation 2*(1/9)^s+ 2*(1/4)^s = 1 for s.

    In this example, the solution sheet gives s = 0.802, but I have no idea how to get to that. Any help much appreciated!
    You can't solve it exactly using logs.

    You could probably get an exact solution using the Lambert W-function. Otherwise, an approximate solution using technology is the best you can do.

    I get s = 0.80276 (so your solution sheet has rounded slightly wrong it would seem).
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  3. #3
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    Thanks for the reply

    I see what you mean about not using logs - now that I look properly the solution sheet says "s = 0.802 (calculator!)", but no more explanation. Can I ask how you got that answer?!
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  4. #4
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    Hello,

    Quote Originally Posted by rory View Post
    Thanks for the reply

    I see what you mean about not using logs - now that I look properly the solution sheet says "s = 0.802 (calculator!)", but no more explanation. Can I ask how you got that answer?!
    I entered it in my calculator
    And I get : 0.802762422212

    Last edited by Moo; May 18th 2008 at 05:44 AM.
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  5. #5
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    Quote Originally Posted by rory View Post
    Thanks for the reply

    I see what you mean about not using logs - now that I look properly the solution sheet says "s = 0.802 (calculator!)", but no more explanation. Can I ask how you got that answer?!
    If you have a graphics calculator (TI-84, say) you can graph Y1 = 2*(1/9)^x+ 2*(1/4)^x and Y2 = 1 and then get the x-coordinate of the intersection point.
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  6. #6
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    Quote Originally Posted by Moo View Post
    [snip]
    And I get : 0.802762422212

    The first 5 decimal places being the same as I gave earlier. The problem sheet has either truncated to three decimal places, or made a mistake in rounding. Because rounding to three decimal places gives 0.803 ......
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