Q.An amplifier has input signal of 0.016W. It produces output of 40W. Calculate the amplifier gain in dB.

The power gain in decibels is $G_p = 10\log_{10}(P_o/P_i)$, so we take the ratio of output to input power and convert. …

[!TLDR]

Take the output-to-input power ratio and apply $G_p = 10\log_{10}(P_o/P_i)$ to get about 33.9 dB.

When the gain of an amplifier is measured in terms of power, it is expressed in decibels as $G_p = 10\log_{10}(P_o/P_i)$, where $P_i$ and $P_o$ are the input and output powers. The logarithmic dB scale is preferred because it matches the ear's logarithmic response and makes large ratios easy to handle.

Given: $P_i = 0.016\,\text{W}$, $P_o = 40\,\text{W}$. …