Exponential and logarithmic functions

There are 30 NRICH Mathematical resources connected to Exponential and logarithmic functions
\pH temperature
problem

Ph temperature

Age
16 to 18
Challenge level
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At what temperature is the pH of water exactly 7?
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.
Extreme dissociation
problem

Extreme dissociation

Age
16 to 18
Challenge level
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In this question we push the pH formula to its theoretical limits.
Drug stabiliser
problem

Drug stabiliser

Age
16 to 18
Challenge level
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How does the half-life of a drug affect the build up of medication in the body over time?
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.
Stirling work
problem

Stirling work

Age
16 to 18
Challenge level
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See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
Cobalt decay
problem

Cobalt decay

Age
16 to 18
Challenge level
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Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.
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.
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.