Exponential and logarithmic functions

There are 30 NRICH Mathematical resources connected to Exponential and logarithmic functions
What's that graph?
problem
Favourite

What's that graph?

Age
14 to 18
Challenge level
filled star filled star empty star

Can you work out which processes are represented by the graphs?

Log Attack
problem
Favourite

Log attack

Age
16 to 18
Challenge level
filled star empty star empty star
Solve these equations.
The Legacy
problem
Favourite

The legacy

Age
14 to 16
Challenge level
filled star filled star empty star
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?
Harmonically
problem
Favourite

Harmonically

Age
16 to 18
Challenge level
filled star filled star filled star
Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
Power match
problem
Favourite

Power match

Age
16 to 18
Challenge level
filled star empty star empty star
Can you locate these values on this interactive logarithmic scale?
Blood buffers
problem
Favourite

Blood buffers

Age
16 to 18
Challenge level
filled star filled star filled star
Investigate the mathematics behind blood buffers and derive the form of a titration curve.
Mixing \pH
problem
Favourite

Mixing ph

Age
16 to 18
Challenge level
filled star empty star empty star
Use the logarithm to work out these pH values
Exponential Trend
problem
Favourite

Exponential trend

Age
16 to 18
Challenge level
filled star empty star empty star
Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.
Back fitter
problem
Favourite

Back fitter

Age
14 to 18
Challenge level
filled star filled star empty star

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Integral Equation
problem
Favourite

Integral equation

Age
16 to 18
Challenge level
filled star empty star empty star
Solve this integral equation.