The document discusses logarithms and different ways of writing numbers as exponents. It shows examples of writing 16 and 625 as exponents in various bases. The key properties of logarithms are then presented, including that the logarithm of a number expressed in a given base is the exponent, and laws such as log(xy) = log x + log y.

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