# Why does log1 0

Although it is possible to choose the basis of the logarithm function freely, three types of logarithm are generally used to solve economic problems:
1. The decadic logarithm log x
With the help of the decadic logarithm, the numerical value of the exponent can be determined if the base corresponds to the number 10. The decadic logarithm is also called the 10's logarithm.
2. The natural logarithm ln x
In contrast to the decadic logarithm, the base of the natural logarithm is Euler's number \$ e \$ with a numerical value of \$ e = 2.71828 \ ldots \$.
3. The binary logarithm or logarithm of two lb (x)
The base of this logarithm is 2. This form of the logarithm is particularly used in computer science, since the number 2 plays an important role in computer architecture.
Logarithms are difficult to determine without tools such as a calculator or without the famous / notorious logarithm table (torment for many earlier generations of students). But if you know the logarithms for a base - e.g. the logarithms of ten with Schülke's table - you can very easily determine the logarithm for another base. The following applies: \ begin {equation} \ log_b (x) = \ frac {\ log_a (x)} {\ log_a (b)} \ end {equation}
example
\$ \ Log_ {10} (256) = 2.408 \$ and \$ \ log_ {10} (2) = 0.3010 \$ can be taken from a logarithm table. Then \ begin {equation} \ log_2 (256) = \ frac {\ log_ {10} (256)} {\ log_ {10} (2)} = \ frac {2,408} {0,3010} = 8 \ end {equation} This result can of course be confirmed quickly, namely \$ 2 ^ 8 = 256 \$