Another way of stating the same fact is
logarithm of b to base a is m If for a positive real number a, a ¹ 1
am = b,
we say that m is the logarithm of b to the base a We write this as 
logab
m ,

“log” being the abbreviation of the word “logarithm” Thus, we have
=
=
=
=
=
=
=
=
3
2
2
3
3
5
0
7
log
8
3,
Since2
8
log
9
2,
Since3
9
log 125
3,
Since5
125
log 1
0,
Since7
1
Laws of Logarithms
In the following discussion, we shall take logarithms to any base a, (a > 0 and a ¹ 1)
First Law: loga
 (mn) = logam + logan
Proof: Suppose that logam = x and logan = y
Then ax= m, ay = n
Hence mn = ax