Exponential and logarithmic functions

$\pH temperature$

problem
pH temperature

Age

16 to 18

Challenge level

At what temperature is the pH of water exactly 7?
$Mixing \pH$

problem
Mixing pH

Age

16 to 18

Challenge level

Use the logarithm to work out these pH values
problem
Blood buffers

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

Can you locate these values on this interactive logarithmic scale?
problem
Harmonically

Age

16 to 18

Challenge level

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
problem
The legacy

Age

14 to 16

Challenge level

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?
problem
Log attack

Age

16 to 18

Challenge level

Solve these equations.
problem
Equation attack

Age

16 to 18

Challenge level

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.
problem
Dating made easier

Age

14 to 16

Challenge level

If a sum invested gains 10% each year how long before it has doubled its value?
problem
What do functions do for tiny x?

Age

16 to 18

Challenge level

Looking at small values of functions. Motivating the existence of the Maclaurin expansion.