Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
-Use the mathematical model for power gain, $G = \log \left( \frac { P _ { 0 } } { P _ { i } } \right) ^ { 10 }$, where $P _ { 0 }$ is the output power in watts and $P _ { i }$ is the input power in watts. Determine the power gain $\mathrm { G }$, in decibels, for an amplifier with an output $\mathrm { P } _ { 0 }$ of 21 watts and an input $P _ { i }$ of $1.2$ watts. Round to five decimal places if necessary.
A) $12.43038 \mathrm {~dB}$
B) $12.96665 \mathrm {~dB}$
C) $13.43038 \mathrm {~dB}$
D) $14.01401 \mathrm {~dB}$

Question

Quizplus · Accepted Answer

The correct answer is A.Explanation:Using the given mathematical model for power gain, we have:$G = \log \left( \frac { P _ { 0 } } { P _ { i } } \right) ^ { 10 }$Substituting the given values, we get:$G = \log \left( \frac { 21 } { 1.2 } \right) ^ { 10 }$Using a calculator, we evaluate this expression to four decimal places:$G = \log \left( \frac { 21 } { 1.2 } \right) ^ { 10 } \approx 12.4304$Therefore, the power gain is approximately 12.4304 decibels.

Use Common Logarithms or Natural Logarithms and a Calculator to Evaluate