Thread: Fractal Geometry - logarithms problem

1. 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!

2. Originally Posted by rory
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).

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?!

4. Hello,

Originally Posted by rory

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

5. Originally Posted by rory