CHAPTER 5 INDICES AND LOGARITHMS

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CHAPTER 5INDICES AND LOGARITHMS

• What is Indices?

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Examples of numbers in index form.

• 33
• (3 cubed or 3 to the power of 3)
• 25
• (2 to the power of 5)
• 3 and 5 are known as indices.
• 2733, 3 is a base and 3 is an index
• 3225, 2 is a base and 5 is an index

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So , why we use indices?

• Indices can make large numbers much more
  manageable, as a large number can be reduced to
  just a base and an index.
• Eg 1,048,576
• 220

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LAWS OF INDICES

• Multiplication of indices with same base
• am ? an am n
• bm n bm ? bn
• Example
• x4 x3 x4 3 x7
• y4y?7 y4(-7) y?3
• 2x3 2x ? 23 8(2x)
• 3y 2 3y ? 3?2

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• Division of indices with same base
• am an am ? n
• bm ? n bm bn
• Example
• c9 ? 4 c5
• 3x-2

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• Raising an index to a power
• (am)n amn
• bmn (bm)n
• EXAMPLE
• (b4)3 b4?3 b12
• (32)3 32?3 36
• (2x)2 22x
• (2y1)3 23y 3
• 32c (3c)2

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• (ab)n an?bn

EXAMPLE (xy)3 x3 ? y3 23 ? 33
63 (ab)-2 a-2 ? b-2
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Law 5

• EXAMPLE

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Other properties of index

• Zero index a0 1, a ? 0
• Negative index a-n
• Fractional index

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Law 5

• EXAMPLE

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Example

• Solve
• 91 x 27
• 2p 1 ? 43 p
• Solve the simultaneous equation
• 2x.42y 8
• 5x.25-y
• (d) 4x3 4x2 6

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Solution

1. x -0.5
2. p 11
3. x -1, y 1
4. x -1.5