Exponential and logarithmic functions

article
Infinite continued fractions

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.
article
What are complex numbers?

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.
problem
Exponential trend

Age

16 to 18

Challenge level

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.
problem
Integral equation

Age

16 to 18

Challenge level

Solve this integral equation.
problem
Tuning and ratio

Age

16 to 18

Challenge level

Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?
problem
How does your function grow?

Age

16 to 18

Challenge level

Compares the size of functions f(n) for large values of n.
problem
Log attack

Age

16 to 18

Challenge level

Solve these equations.
problem
Prime counter

Age

16 to 18

Challenge level

A short challenge concerning prime numbers.
problem
Sierpinski triangle

Age

16 to 18

Challenge level

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.
problem
Stirling work

Age

16 to 18

Challenge level

See how enormously large quantities can cancel out to give a good approximation to the factorial function.