system (and the properties of logarithms) makes the mathematics involved in some equations much simpler. For instance,
recall the Friis Transmission Formula:|
To convert this equation from linear units in Watts to decibels, we take the logarithm of both sides and multiply by 10:
A nice property of logarithms is that for two numbers A and B (both positive), the following result is always true:
Equation (*) then becomes:
Using the definition of decibels, the above equation becomes a simple addition equation in dB:
The above representation is easier to work with, which is kind of cool.