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1. LOGARITHMS

2. 16 =
4
2
16 =
2
4
16 =
1
16
625 =
4
5
625 =
2
25
625 =
1
625

3. 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

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

5. LET’S SEE THE DIFFERENT WAYS OF
WRITING 16 AS AN EXPONENT
The power of 16
when expressed in base 16
is 1
1=
16
16

6. LET’S SEE THE DIFFERENT WAYS OF
WRITING 16 AS AN EXPONENT
The power of
16
when expressed in
base2
Is
4
24 = 16

7. LET’S SEE THE DIFFERENT WAYS OF
WRITING 16 AS AN EXPONENT
The power of
16
when expressed in base4
Is
2
42 = 16

8. LET’S SEE THE DIFFERENT WAYS OF
WRITING 16 AS AN EXPONENT
The power of
16
when expressed in base
16
Is
1
161 = 16

9. Now try to express the following in
‘log’form
The power of 625 when
expressed in base 5 is 4
54 = 625

10. Now try to express the following in
‘log’form
The power of 625 when
expressed in base 25 is 2
252 = 625

11. Now try to express the following in
‘log’form
The power of 625 when
expressed in base 625 is 1
6251 = 625

12. 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

13. 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

14. 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

15. 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

16. 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