An amplifier has an input power of 5 mW. The output power is 100 mW. What is the decibel gain to the nearest decibel?

gain = 10log(100/5) = 10log20 = 13dB

Well, if you're looking for the "nearest decibel," I'm afraid you'll have to become a "decibel detective." Just kidding, I'll help you out!

To find the decibel gain, we can use the formula:

Gain (in decibels) = 10 log (output power / input power)

Plugging in the given values:

Gain (in decibels) = 10 log (100 mW / 5 mW)

Now, let's put our math hats on and calculate this:

10 log (20) ≈ 13.98 decibels

So, to the nearest decibel, the gain of the amplifier is approximately 14 decibels. Just remember, in the wacky world of clowns and amplifiers, the gain is always measured in decibels!

To find the decibel gain, we can use the formula:

Gain (in decibels) = 10 * log10 (Output Power / Input Power)

Given that the input power is 5 mW and the output power is 100 mW, we can substitute these values into the formula:

Gain (in decibels) = 10 * log10 (100 mW / 5 mW)

Simplifying,

Gain (in decibels) = 10 * log10 (20)

Using a calculator, we can find that log10 (20) is approximately 1.3010.

Therefore,

Gain (in decibels) = 10 * 1.3010 = 13.010 decibels.

To the nearest decibel, the decibel gain of the amplifier is approximately 13 decibels.

To calculate the decibel gain, we need to use the formula:

Gain (in decibels) = 10 * log10(Output Power / Input Power)

In this case, the input power is 5 mW and the output power is 100 mW. Let's substitute these values into the formula to find the gain in decibels:

Gain (in decibels) = 10 * log10(100 mW / 5 mW)

First, let's simplify the fraction inside the logarithm:

Gain (in decibels) = 10 * log10(20)

Now, we can use a calculator to evaluate the logarithm:

Gain (in decibels) ≈ 10 * 1.3010

Multiply the values:

Gain (in decibels) ≈ 13.0100

Rounded to the nearest decibel, the decibel gain is 13 dB.