# MATHEMATICS CLASS FOR CLASS 9-12

## CHAPTER 1: - INDICES AND LOGARITHMS(JSS3 AND SS1)

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Topic: MathsGE With MeyiBule

CHAPTER 1: - INDICES AND LOGARITHMS(JSS3 AND SS1)

LAWS OF INDICES(PART 1)

The following laws of indices are true for all values of n, I and x ≠0.

1.                              xn × x? = xn??

2.                              xn ÷ x? = xn??

3.                              x° = 1, x ≠0

4.                              x-n =

5.                              (xn)? = xn?

6.                              x =

7.                              x =  or ()n

EXAMPLE 1

Simplify

a.                              10× 10³

b.                              22n7 ÷ 2n³

c.                                19°

d.                              5?2

e.                              2³ × ()?¹

f.       r × r° × r?5.

a)                                102 × 10³ = (10 × 10) × (10 × 10 × 10)

= 10 × 10 × 10 × 10 × 10

= 105

Check: 102 × 103 = 102+3 = 105                                                                             (Law 1)

b)                             22n7 ÷ 2n3 =  × n7-3 = 11n4                                                                      (Law 2)

Check:

22n7 ÷ 2n3

=

= 11 × n × n × n × n = 11 × n4

= 11n4

a)                              190 = 1                                                                                                          (Law 3)

Check:

190 = 19n-n    (since n – n = 0)

=                                                                                                         (Law 2)

= 1 (num. and denom. are equal)

b)                             5?2  =   =                                                                                                  (Law 4)

Check:

5?2  = 5°?²

=                                                                                                            (Law 2)

=                                                                                                            (Law 3)

=

c)                               23 × () ?¹ = 8 ×                                                                                             (Law 4)

= 8 × 6 = 48

d)                             r × r° × r?5 = r1?°?(?5)                                                                                      (Law 1)

= r?4 =

or      r × r° × r?5 = r1 × 1 ×                                                                                   (Laws 3

=                                                                                                 and 4)

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AUTHOR: EBULE PRECIOUS ORITSEMEYIWA

LOCATION: WARRI, DELTA STATE

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