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# 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. logx (YZ) = logx Y + logx Z
2. logx ($\frac{Y}{Z}$) = logx Y - logx Z
3. logx Ym = m logx Y

These laws can be explained by some examples:

Example 1:

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

Example 2:

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