PPT: Logarithms

``` Page 1

LOGARITHMS

Page 2

LOGARITHMS

INDICES
? Any expression written as a
n
is defined as the
variable a raised to the power of the number n

? n is called a power, an index or an exponent of a

? Example - where n is a positive whole number,
a
1
= a
a
2
= a ? a
a
3
= a ? a ? a
a
n
= a ? a ? a ? a……n times

Page 3

LOGARITHMS

INDICES
? Any expression written as a
n
is defined as the
variable a raised to the power of the number n

? n is called a power, an index or an exponent of a

? Example - where n is a positive whole number,
a
1
= a
a
2
= a ? a
a
3
= a ? a ? a
a
n
= a ? a ? a ? a……n times

INDICES SATISFY THE FOLLOWING RULES
? a
n
= a ? a ? a ? a……n times
e.g. 2
3
= 2 ? 2 ? 2  = 8

?Negative powers…..

a
-n
=

e.g. a
-2
=

e.g. where a = 2
2
-1
=    or   2
-2
=
n
a
1
2
1
a
2
1
4
1
2 2
1
?
?
Page 4

LOGARITHMS

INDICES
? Any expression written as a
n
is defined as the
variable a raised to the power of the number n

? n is called a power, an index or an exponent of a

? Example - where n is a positive whole number,
a
1
= a
a
2
= a ? a
a
3
= a ? a ? a
a
n
= a ? a ? a ? a……n times

INDICES SATISFY THE FOLLOWING RULES
? a
n
= a ? a ? a ? a……n times
e.g. 2
3
= 2 ? 2 ? 2  = 8

?Negative powers…..

a
-n
=

e.g. a
-2
=

e.g. where a = 2
2
-1
=    or   2
-2
=
n
a
1
2
1
a
2
1
4
1
2 2
1
?
?
? A Zero power
a
0
= 1
e.g. 8
0
= 1

? A Fractional power

e.g.

n
a a
n
?
1
3 9 9 9
2
2
1
? ? ?
2 8 8
3
3
1
? ?
Page 5

LOGARITHMS

INDICES
? Any expression written as a
n
is defined as the
variable a raised to the power of the number n

? n is called a power, an index or an exponent of a

? Example - where n is a positive whole number,
a
1
= a
a
2
= a ? a
a
3
= a ? a ? a
a
n
= a ? a ? a ? a……n times

INDICES SATISFY THE FOLLOWING RULES
? a
n
= a ? a ? a ? a……n times
e.g. 2
3
= 2 ? 2 ? 2  = 8

?Negative powers…..

a
-n
=

e.g. a
-2
=

e.g. where a = 2
2
-1
=    or   2
-2
=
n
a
1
2
1
a
2
1
4
1
2 2
1
?
?
? A Zero power
a
0
= 1
e.g. 8
0
= 1

? A Fractional power

e.g.

n
a a
n
?
1
3 9 9 9
2
2
1
? ? ?
2 8 8
3
3
1
? ?
ALL INDICES SATISFY THE
FOLLOWING RULES IN MATHEMATICAL
APPLICATIONS

Rule 1  a
m
. a
n
= a
m+n
e.g.   2
2
. 2
3
= 2
5
= 32
e.g.   5
1
. 5
1
= 5
2
= 25
e.g.   5
1
. 5
0
= 5
1
= 5

Rule 2

n m
n
m
a
a
a
?
?
8 2 2
2
2
2
2 2 2
2
2
1
3 0 3
0
3
1 2 3
2
3
? ? ?
? ? ?
?
?
. .
. .
g e
g e
```

## Physics for JEE Main & Advanced

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## Physics for JEE Main & Advanced

289 videos|635 docs|179 tests

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