�ݺ�ߣ

16 =

4
2

16 =

2
4

16 =

1
16

625 =

4
5

625 =

2
25

625 =

1
625

LET’S SEE THE DIFFERENT WAYS OF
WRITING 16 AS AN EXPONENT
The power of 16
when expressed in base 2
is 4

4=
2

16

The power of 16
is 2

2=
4

16

The power of 16
is 1

1=
16

16

The power of
16
when expressed in
base2
Is
4

24 = 16

The power of
16
when expressed in base4
Is
2

42 = 16

The power of
16
when expressed in base
16
Is
1

161 = 16

Now try to express the following in
‘log’form
The power of 625 when
expressed in base 5 is 4

54 = 625

‘log’form

252 = 625

‘log’form

6251 = 625

In general....
• The power of a number “a” when expressed
in base “b”, is “c”.
• In exponential form, we write:
• In ‘log’ form, we should write:

c

b =a

Let’s play with log...

log 125 = 3 log 49 = 2
?
?
5
7
?
?
log 256 = 8 log 64 = 3
4
2
log 81 = 4
?
3

Laws of logarithms:

Let am = x
an =y
Then,
m an
a
m+n
a

log a x = m
log a y = n

= xy
= xy

log a xy = m + n = log a x +log a y

Let am = x
an =y
Then,

log a x = m
log a y = n

m/ an
a
m- n
a

= x/y
= x/y

log a x/y = m - n = log x - log y
a
a

Let am = x

log a x = m

Then,
m )n = x n
(a

am n = x n
log a xn = mn =(log x)xn
a

�ݺ�ߣ

Logarithms

Recommended

More Related Content

Viewers also liked (7)

Recently uploaded (20)

Logarithms