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Broad Topics > Sequences, Functions and Graphs > Logarithmic functions

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Mixing Ph

Stage: 5 Challenge Level: Challenge Level:1

Use the logarithm to work out these pH values

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Blood Buffers

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Power Match

Stage: 5 Challenge Level: Challenge Level:1

Can you locate these values on this interactive logarithmic scale?

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Harmonically

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Log Attack

Stage: 5 Challenge Level: Challenge Level:1

Solve these equations.

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Equation Attack

Stage: 5 Challenge Level: Challenge Level:1

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.

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Drug Stabiliser

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Weekly Challenge 44: Prime Counter

Stage: 5 Challenge Level: Challenge Level:1

A weekly challenge concerning prime numbers.

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Extreme Dissociation

Stage: 5 Challenge Level: Challenge Level:1

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

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Ph Temperature

Stage: 5 Challenge Level: Challenge Level:1

At what temperature is the pH of water exactly 7?

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What Do Functions Do for Tiny X?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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How Does Your Function Grow?

Stage: 5 Challenge Level: Challenge Level:1

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

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Sierpinski Triangle

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Complex Sine

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Big, Bigger, Biggest

Stage: 5 Challenge Level: Challenge Level:1

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


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