Decibels

Two levels of power can be compared using a unit of measure called the bel, In communications systems, gain is measured in bels, which is defined by the following equation:
$$\mathrm{B}=\log _{10} \frac{P_{2}}{P_{1}}$$
However, to provide a unit of measure of less magnitude, a decibel is defined, where
$$1 \text { bel }=10 \text { decibels }(\mathrm{dB})$$
The result is the following important equation, which compares power levels $ P_{2} $ and $ P_{1} $ in decibels:
$$\bbox[10px,border:1px solid grey]{\mathrm{dB}=10 \log _{10} \frac{P_{2}}{P_{1}} \text { decibels }(\mathrm{dB}) } \tag{1}$$