How to Convert between dB Voltage and Power
When talking about power quantities, we use the following formula:

\$ 10\log_{10}(P/P_0)dB \$

Which defines the decibel ratio in terms of power units.

However, when we deal with voltages, we actually compare the ratio of the squares of the voltages (because power is proportional to voltage squared, and it is useful for both decibel formulations to give the same results) which gives us:

\$10\log_{10}(V^{2}/V_0^{2})dB =  10\log_{10}[(V/V_0)^{2}] \$

According to the list of logarithmic identities, \$\log(a^{x}) = x\log(a) \$, so we get \$2*10\log_{10}(V/V_0) = 20\log_{10}(V/V_0) \$