To solve this problem, we need to determine the voltage gain and power gain of the common-emitter transistor amplifier.$\\$Given:$\\$• Audio signal voltage across the collector $V_c = 3 \,$V$\\$• Collector resistance $R_c = 3 \,$k$\Omega = 3000 \, \Omega \\$• Current gain ($\beta$) $= 100 \\$• Base resistance $R_b = 2 \,$k$\Omega = 2000 \, \Omega \\$Step 1: Calculate the input voltage $V_{in}. \\$The input current $I_b = \frac{V_{in}}{R_b}. \\$The output current $I_c = \beta \cdot I_b. \\$The voltage across the collector is given by $V_c = I_c \cdot R_c. \\$Substitute $I_c = \beta \cdot I_b = \beta \cdot \frac{V_{in}}{R_b}: \\ V_c = \beta \cdot \frac{V_{in}}{R_b} \cdot R_c \\$Rearrange to solve for $V_{in}: \\ V_{in} = \frac{V_c \cdot R_b}{\beta \cdot R_c} \\$Substitute the known values:$\\ V_{in} = \frac{3 \cdot 2000}{100 \cdot 3000} \\ V_{in} = \frac{6000}{300000} \\ V_{in} = 0.02 \,$V$\\$Step 2: Calculate the voltage gain $A_v. \\ A_v = \frac{V_c}{V_{in}} \\ A_v = \frac{3}{0.02} \\ A_v = 150 \\$Step 3: Calculate the power gain $A_p. \\$Power gain is given by $A_p = A_v \cdot \beta. \\ A_p = 150 \cdot 100 \\ A_p = 15000 \\$Therefore, the voltage gain is 150 and the power gain is 15000.$\\$This corresponds to Option 2.