Solution:

$ \begin{aligned} P(0) & =2 \text { mwatt }=2 \times 10^{-3} \text { watt } \\\\ P(z) & =2 \mu \mathrm{watt}=2 \times 10^{-6} \text { watt } \\\\ \alpha & =0.5 \mathrm{~dB} / \mathrm{km}\\ \end{aligned} $

$ \alpha=10 \times \frac{1}{z}\left[\frac{p(0)}{p(z)}\right]\\ $

$ \begin{aligned} & 0.5=\frac{1}{\mathrm{z}} \mathrm{x} 3 \\\\ & \mathrm{z}=\frac{3}{0.05}\\ \end{aligned} $