Exponential and logarithmic functions

There are 30 NRICH Mathematical resources connected to Exponential and logarithmic functions
Tuning and Ratio
problem

Tuning and Ratio

Age
16 to 18
Challenge level
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Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?
Integral Equation
problem

Integral Equation

Age
16 to 18
Challenge level
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Solve this integral equation.
Sierpinski Triangle
problem

Sierpinski Triangle

Age
16 to 18
Challenge level
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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.
Exponential Trend
problem

Exponential Trend

Age
16 to 18
Challenge level
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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.
Complex Sine
problem

Complex Sine

Age
16 to 18
Challenge level
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Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.
Big, Bigger, Biggest
problem

Big, Bigger, Biggest

Age
16 to 18
Challenge level
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Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?
What are Complex Numbers?
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.
Infinite Continued Fractions
article

Infinite Continued Fractions

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