Question

If $R_c = m \times \ln \left(1 + \frac{R_m}{m} \right)$ then $R_m$ is equal to

• A. $R_m = \ln \left(1 + \frac{R_c}{m} \right)$
• B. $R_m = \ln \left(1 + \frac{R_c}{e} \right)$
• C. $R_m = m \left( e^{\frac{R_c}{m}} - 1 \right)$
• D. Cannot be determined

Answer 1

Answer: (C)

$R_m = m \left( e^{\frac{R_c}{m}} - 1 \right)$

Answer 2

Given the equation $R_c = m \times \ln \left(1 + \frac{R_m}{m} \right)$, we need to solve for $R_m$.
1. Start by dividing both sides by $m$:
$\frac{R_c}{m} = \ln \left(1 + \frac{R_m}{m} \right)$
2. Exponentiate both sides to remove the natural logarithm:
$e^{\frac{R_c}{m}} = 1 + \frac{R_m}{m}$
3. Subtract 1 from both sides:
$e^{\frac{R_c}{m}} - 1 = \frac{R_m}{m}$
4. Multiply both sides by $m$ to solve for $R_m$:
$R_m = m \left( e^{\frac{R_c}{m}} - 1 \right)$
Thus, the correct option is C: $R_m = m \left( e^{\frac{R_c}{m}} - 1 \right)$.