Exponential and logarithmic functions

In this question we push the pH formula to its theoretical limits.

At what temperature is the pH of water exactly 7?

Use the logarithm to work out these pH values

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

Can you locate these values on this interactive logarithmic scale?

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

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?

Solve these equations.

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.

If a sum invested gains 10% each year how long before it has doubled its value?