This document discusses logarithms and their use in different number systems. It explains that logarithms describe the exponent that a base number must be raised to to equal the original number. It provides examples of logarithms with base 10 and base 2. It also introduces the topic of material properties diagrams and case studies but does not provide details about these topics.

1. Logarithms
• We live in a log base 10 world we measure
and count in powers of ten.
100 = 1 log10(1) = 0
101 = 10 log10(10) = 1
102 = 100 log10(100) = 2
103 = 1,000 log10(1,000) = 3
104 = 10,000 log10(10,000) = 4
105 = 100,000 log10(100,000) = 5

2. Logarithms
• Binary uses base 2. Now, work out the
20 = 1 log2(1) = 0 first 5 numbers in log
21 = 2 log2(2) = 1 base 5.
22 = 4 log2(4) = 2
23 = 8 log2(8) = 3
24 = 16 log2(16) = 4
25 = 32 log2(32) = 5

3. Materials and
Case Studies

4. Material Properties Diagrams
• Which materials are
the toughest
• Which materials are
the strongest
• Which are the weakest
and the most brittle?
• How do we know that
a logarithmic scale is
being used?

5. Top Tips for Case Studies
• Look at the properties we have discussed in
lessons (strength, toughness, elasticity….)
• Discuss the applications of the material
• Make sure you understand EVERYTHING you
have written down on the sheet
• Including properties like Young’s Modulus
would be beneficial
• You have until the first week of December to
get this done