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CHAPTER 5 INDICES AND LOGARITHMS

CHAPTER 5 INDICES AND LOGARITHMS. What is Indices?. Examples of numbers in index form. 3 3 (3 cubed or 3 to the power of 3) 2 5 (2 to the power of 5) 3 and 5 are known as indices. 27=3 3 , 3 is a base and 3 is an index 32=2 5 , 2 is a base and 5 is an index.

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CHAPTER 5 INDICES AND LOGARITHMS

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  1. CHAPTER 5INDICES AND LOGARITHMS What is Indices?

  2. 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. 27=33, 3 is a base and 3 is an index 32=25, 2 is a base and 5 is an index

  3. 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

  4. LAWS OF INDICES Multiplication of indices with same base: am  an = am + n bm + n =bm  bn Example: x4x3 = x4 + 3 = x7 y4y7 = y4+(-7) = y3 = 2x+3= 2x 23 = 8(2x) 3y – 2 = 3y32 =

  5. Division of indices with same base: am ÷ an = am  n bm  n =bm ÷ bn Example: = c9  4 = c5 3x-2 =

  6. 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 (2y+1)3 = 23y + 3 32c = (3c)2

  7. EXAMPLE: (xy)3 = x3  y3 23  33 = 63 (ab)-2 = a-2  b-2 (ab)n = anbn

  8. Law 5: EXAMPLE:

  9. Other properties of index Zero index: a0 = 1, a 0 Negative index: a-n Fractional index:

  10. Law 5: EXAMPLE:

  11. Example Solve • 91 – x = 27 • 2p + 1  43 – p = • Solve the simultaneous equation 2x.42y = 8 5x.25-y = (d) 4x+3 – 4x+2 = 6

  12. Solution • x = -0.5 • p = 11 • x = -1, y = 1 • x = -1.5

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