The power of a transmitter is increased from 5 watts to 50 watts by a linear amplifier. The power gain, expressed in dB, is:

A fundamental rule of thumb for decibels is that a tenfold increase (or decrease) in power corresponds exactly to a 10 dB change. The power ratio in this scenario is 50 watts divided by 5 watts, which equals a ratio of 10. Using the decibel formula for power, you calculate 10 * log10(10). Since the logarithm of 10 is 1, multiplying that by 10 results in 10 dB. Distractors like 45 dB are designed to trick you into just subtracting the two wattages (50 watts - 5 watts = 45), but decibels represent a logarithmic ratio (multiplication or division), not simple addition or subtraction.