In this section, student will learn evaluating logarithm.
The word logarithm was coined from two Greek words"logos" which means a ratio and "arithmos" means numbers.
Logarithms and exponents are closely related to each other. The inverse of these operations gives us two distinct operations viz. extracting roots and taking logarithms.

a^{m} = b is exponential form.

It is read as mth power of 'a' is 'b'.
For each positive real number a, a≠ 1, the unique real number 'm' is called the logarithm of 'b' to the base 'a' or

log_{a}b = m if and only if a^{m} = b

'log' being the abbreviation of the word 'logarithm.

Properties of logarithm
1) log_{a}1 = 0 because a^{0}=1
2) log_{a}a = 1 because a^{1}=a
3) log_{a}a^{x} = x because a^{x} =a^{x}

Evaluating logarithm

1) log_{3}27 Solution : We know from definition that
log_{a}b = m, if and only if a^{m} = b, a > 0 and a≠1
Let m = log_{3}27
∴ 3^{m} = 27
3^{m} = 3^{3}
∴ m = 3
so, log_{3}27= 3

2) log_{2}√(32) Solution : We know from definition that
log_{a}b = m, if and only if a^{m} = b, a > 0 and a≠1
Let m = log_{2}√(32)
∴ 2^{m} = √(32)
2^{m} = (2^{5})^{1/2}
2^{m} = 2^{5/2}
∴ m = 5/2
so, log_{2}√(32)= 5/2