A logarithmic system which reveals the number of multiplying factors when a number is expressed as multiplying factors on the basis of $2$, is called binary logarithm.
Michael Stifel (or Styfel) was a German mathematician who introduced the system of a logarithms by taking as its base. The original meaning of binary is two pieces or two parts. Due to the usage of as base in logarithmic system, the logarithmic system is known as Binary logarithmic system.
The value of base is neither equal to nor belongs to negative real numbers group but it belongs to positive real numbers. These can be expressed in mathematical form.
and but .
The conditions made number is eligible to use as base in logarithm system as per the principle definition of the logarithms.
Assume, the number and the independent algebraic variable are involved in forming an exponential form expression by becoming base and power respectively. Also, assume the value of to the power is equal to another variable . It can be expressed in mathematical form.
According to definition of the logarithmic system, the logarithm of to base equals to . It is written as given here.
The relation between exponential form expression and binary logarithmic system can be expressed in mathematical form.