Logs

Example: 10^2=100. We say 2 is the log of 100 to base 10.

Log is the abbreviation for logarithm.

The logarithm is an operator that is used to find at which power you have to raise a number to get another.

In other words,

\(\forall n\in \mathbb{R}_{+}^{*},\forall b\in \mathbb{R}_{+}^{*}, \\\text{If } \log_b(n)=p\text{, then }b^p=n.\)

(The number b is called the base of the logarithm.)

Examples:

1. log₂(16)=4 because 2⁴=16
2. log₁₀(100)=2 because 10²=100
3. log_e(e⁸) is 8*.

*The number e is an irrationnal number called Euler's number (e≈2.71828182845904523536028747135266249775724709369995...). The logarithm of a number n to base e is also called natural logarithm of n and written ln(n).

The LOG of a number is the exponent of 10  you would use to get that number.