Answer
$$\frac{\pi}{4} d^{2} L=\frac{\pi}{4} d_{1}^{2} L_{0}$$
$$\frac{L}{L_{0}}=\frac{d_{1}^{2}}{d^{2}}=\left(\frac{d_{1}}{d}\right)^{2}$$
$$\varepsilon_{t}=\ln \frac{L}{L_{0}}=\ln \left(\frac{d_{1}}{d}\right)^{2}$$
$$\varepsilon_{t}=2 \ln \frac{d_{1}}{d}$$
Work Step by Step
$$\frac{\pi}{4} d^{2} L=\frac{\pi}{4} d_{1}^{2} L_{0}$$
$$\frac{L}{L_{0}}=\frac{d_{1}^{2}}{d^{2}}=\left(\frac{d_{1}}{d}\right)^{2}$$
$$\varepsilon_{t}=\ln \frac{L}{L_{0}}=\ln \left(\frac{d_{1}}{d}\right)^{2}$$
$$\varepsilon_{t}=2 \ln \frac{d_{1}}{d}$$
