# Resources tagged with: Exponential and Logarithmic Functions

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### There are 26 results

Broad Topics > Coordinates, Functions and Graphs > Exponential and Logarithmic Functions

### Gosh Cosh

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

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

### What Do Functions Do for Tiny X?

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

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

### Prime Counter

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

A short challenge concerning prime numbers.

### Cobalt Decay

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

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

### Complex Sine

##### 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.

### Log Attack

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

Solve these equations.

### Integral Equation

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

Solve this integral equation.

### 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.

### Hyperbolic Thinking

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

Explore the properties of these two fascinating functions using trigonometry as a guide.

### Quorum-sensing

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

This problem explores the biology behind Rudolph's glowing red nose.

### 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 ?

### What Are Complex Numbers?

##### Age 16 to 18

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and. . . .

### How Does Your Function Grow?

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

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

### Function Pyramids

##### 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?

### Exponential Trend

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

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.

### Sierpinski Triangle

##### 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.

### Tuning and Ratio

##### 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?

### Mixing Ph

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

Use the logarithm to work out these pH values

### Ph Temperature

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

At what temperature is the pH of water exactly 7?

### Extreme Dissociation

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

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

### Blood Buffers

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

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

### Big, Bigger, Biggest

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

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

### Drug Stabiliser

##### 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?

### Power Match

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

Can you locate these values on this interactive logarithmic scale?

### Infinite Continued Fractions

##### Age 16 to 18

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.

### 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?