### There are 17 results

Broad Topics >

Functions and Graphs > Logarithmic functions

##### 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.

##### Age 16 to 18 Challenge Level:

What is the total area of the triangles remaining in the nth stage
of constructing a Sierpinski Triangle? Work out the dimension of
this fractal.

##### Age 16 to 18 Challenge Level:

Solve these equations.

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

##### Age 16 to 18 Challenge Level:

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.

##### Age 16 to 18 Challenge Level:

Why is the modern piano tuned using an equal tempered scale and
what has this got to do with logarithms?

##### Age 16 to 18 Challenge Level:

Compares the size of functions f(n) for large values of n.

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Can you locate these values on this interactive logarithmic scale?

##### Age 16 to 18 Challenge Level:

Use the logarithm to work out these pH values

##### Age 16 to 18 Challenge Level:

At what temperature is the pH of water exactly 7?

##### Age 16 to 18 Challenge Level:

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

##### 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 ?

##### Age 16 to 18 Challenge Level:

How does the half-life of a drug affect the build up of medication
in the body over time?

##### Age 16 to 18 Challenge Level:

A short challenge concerning prime numbers.

##### Age 16 to 18 Challenge Level:

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