Exponential and logarithmic functions

Investigate the mathematics behind blood buffers and derive the form of a titration curve.

Use the logarithm to work out these pH values

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

Explore the properties of these two fascinating functions using trigonometry as a guide.

This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.

A short challenge concerning prime numbers.

Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?

At what temperature is the pH of water exactly 7?

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.