A logarithm is a power to which a number must be raised in order to get some other

number.

In other words, if a is a positive real number, other than 1 and a^m = x,

then we write: m = log_a x

and we say that the value of log x to the base a is m.

Ex 1. 10³ = 1000 => log₁₀ 1000 = 3

Ex 2. 3⁴ = 81 => log₃ 81 = 3

Ex 3. 2^-3 = 1/8 => log₂ (1/8) = -3

There are some rules in logarithm listed below:

1.  log_a (x * y) = log_a x + log_a y

2.  log_x x = 1

3.  log_a (x/y) = log_a x - log_a y

4.  log_a 1 = 0

5.  log_a (x^p ) = p * log_a x

6.  log_a x = 1/log_x a

7.  log_a x = log_b x/log_b a = log x/log a

It is assumed that when base is not given, it is taken as 10