Exponential and logarithmic functions

Solve this integral equation.

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

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.

Solve these equations.

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?

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

Can you locate these values on this interactive logarithmic scale?

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