ratio and proportion, indices and logarithm part 3
TRANSCRIPT
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Ratio and Proportion, Indices and Logarithm
CPT Section D Quantitative Aptitude Chapter 1 Part III: Indices
Ms. Ritu Gupta MA (Maths)
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Indices
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Learning Objectives
Meaning of Indices and
their Application
Laws of Indices which
facilitates their easy
applications
Laws of Surds
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Indices
If a is a non-zero real number and n is a positive integer, then
a X a X a X …………………… n times is represented as an where, a is called the base and n is called the exponent or power or index.
Similarly (a X a X a X …………………… n times) (b X b X b X ………………… m times) will be represented as anbm
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Laws of Indices
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Laws of Indices- Continued
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Surds
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Equality Of Surds
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Laws of Surds
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Laws of Surds - Continued
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Results
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Identities
(a +b)2 = a2 + b2 + 2ab
(a -b)2 = a2 + b2 - 2ab
(a +b) (a-b) = a2 – b2
(a+b+c)2 = a2 + b2 + c2 +2ab + 2bc +2ca
(a + b)3 = a3 + b3 + 3ab (a+b) or
(a + b)3 = a3 + b3 + 3a2b +3ab2
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Identities - Continued
(a – b)3 = a³ - b³- 3ab(a – b) or
(a – b)3 = a³ - b³- 3a²b + 3ab²
a³ + b³ = (a+b) (a² - ab + b²)
a³ - b³ = (a-b) (a² + ab + b²)
Note: If we want to find a² + b²
Then we know (a+b)² = a² + b² + 2ab
a² + b² = (a+b)² - 2ab
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Illustrations
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Illustration 1
Simplify: 32 × (8)-4/3
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Solution: 32 × (8)-4/3 = 25 × (2³)-4/3 = 25 × (2)-4 = 25-4 = 2
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Illustration 2
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Illustration 3
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Illustration 3 - Continued
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Illustration 4
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Illustration 4 - Continuded
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Illustration 4 - Continuded
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Illustration 5
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Illustration 6
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Illustration 6 - Continued
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Illustration 7
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Illustration 8
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Illustration 9
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Illustration 9 - Continued
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Illustration 10
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Illustration 10 - Continued
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Illustration 11
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Illustration 11 - Continued
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Illustration 12
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Illustration 13
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Illustration 14
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Illustration 14 - Continued
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THANK YOU
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