College Algebra Related Pages: 396-397 "Solving an Exponential Equation," Examples 1 & 2
Trigonometry Related Pages: 423-424 "Solving an Exponential Equation," Examples 1 & 2
College Algebra and Trigonometry Related Pages: 396-397 "Solving an Exponential Equation," Examples 1 & 2
Precalculus Related Pages: 314-315 "Solving an Exponential Equation," Examples 1 & 2

This activity allows you to explore an application of solving an exponential equation using logarithms. You will learn how to calculate the fractal dimension of a series of regular fractals without access to a calculator.

Calculation of fractal dimension is based upon the fact that Dimension (D), Scale (S) and Number (N) of similar copies in a geometric fractal follows the exponential equation:

For example, the Koch Snowflake

is built from replacing a line segment with 4 segments each 1/3 as long as the original, arranged as:

The scale factor is 3 and the number of identical copies in the replacement is 4. Hence, we need to solve the exponential equation for D so that

In this case to find D, take the natural log of both sides of the equation.
ln 3^D = ln 4 therefore
D = ln 4/ln 3
which is about 1.262.