Laws of Logarithms

TopLogarithm increases the number, or we simply say it is a power of log value which changes the number in increasing order. Lets now study on the rules of Logarithm. Now suppose we have a positive number ‘x’, and this positive number is not equals to 1. Now suppose ‘m’ is a real number and ‘Y’ and ‘Z’ is a real positive number.

The rules for logarithms are given below:

1. log_x (YZ) = log_x Y + log_x Z
2. log_x ($\frac{Y}{Z}$) = log_x Y - log_x Z
3. log_x Y^m = m log_x Y

These laws can be explained by some examples:

Example 1:

log₂ (8 * 4)
= log₂ 8 + log₂ 4        [using the 1^st law]
= log₂ 2³ + log₂ 2²
= 3log₂ 2 + 2log₂ 2   [using the 3^rd law]
= 3 + 2
= 5

Example 2:

log₂ ($\frac{8}{4}$)
= log₂ 8 - log₂ 4         [using the 2^nd law]
= log₂ 2³ - log₂ 2²
= 3log₂ 2 - 2log₂ 2    [using the 3^rd law]
= 3 - 2
= 1