What is the approximate amount of change, measured in decibels (dB), of a power increase from 20 watts to 200 watts?

To determine the change in power level in decibels (dB) when moving from one power level to another, you can use the formula:

[ dB = 10 \times \log_{10}(\frac{P2}{P1}) ]

In this case, you're increasing power from 20 watts to 200 watts. Plugging these values into the formula gives:

[ dB = 10 \times \log_{10}(\frac{200}{20}) ]

First, simplify the fraction:

[ \frac{200}{20} = 10 ]

Now, calculate the logarithm:

[ \log_{10}(10) = 1 ]

So, substituting back into the formula:

[ dB = 10 \times 1 = 10 ]

Therefore, the change in power from 20 watts to 200 watts is approximately 10 dB. This indicates that a tenfold increase in power corresponds to a 10 dB increase in signal level, which accurately reflects the logarithmic nature of decibel measurements.