A decibel (dB) is 1/10th of a bel (B), so 10 decibel = 1 bel. A decibel value by itself does not mean anything. It expresses a ratio, typically of power or intensity, on a logarithmic scale.
In electronics, voltage and current amplification are calculated as 20 * log10 and power as 10 * log10. Logarithms are the inverse of exponentiation. For instance, the logarithm to the base 10 of a number is the power to which 10 must be raised to produce that number.
For example, since 102 = 100, the logarithm base 10 of 100 is 2, or log10 (100) = 2.
To calculate the amplification of voltage by a factor of 100, we apply this formula: 20 * log10 (100) = 20 * 2 = 40 dB.
And a factor of 10 is calculated as 20 * log10 (10), which is 20 dB.
Double the factor is 20 * log10(2). You need to look up (or use a calculator), what the value of x is for this equation. 10x = 2. It's approximately 0.301. Because 20 * 0.301 is close to 6, in electronics 6dB is considered as doubling the factor.