Solution:

α = 3 dB/km

$ \frac{p(0)}{p(z)}=50 \%=0.5\\ $

a) Power decreases by 50 %:

$ \begin{aligned}\\ & {\left[\frac{200 \mu \mathrm{W}}{\mathrm{P}(\mathrm{z})}\right]=10^{2.4}} \\\\ & 3=10 \cdot \frac{1}{\mathrm{z}} \log [0.5]\\ \end{aligned}\\ $

z = 1 km… Ans.

$ \text { b) } \frac{\mathrm{p}(0)}{\mathrm{p}(\mathrm{z})}=25 \%=0.25 \text { Since power decrease by } 75%: $

$ \begin{array}{r} 3=10 \times \frac{1}{z} \log [0.25] \\\\ z=\mathbf{2} \text { km... Ans. } \\ \end{array} $