Answer
First we use $$\Delta \beta_{12}=\beta_{1}-\beta_{2}=(10 \mathrm{dB}) \log \left(I_{1} / I_{2}\right)$$
Since $$\Delta \beta_{12}=(10 \mathrm{dB}) \log \left(I_{1} / I_{2}\right)=37 \mathrm{dB},$$ we get
$$
I_{1} / I_{2}=10^{37} \mathrm{dB} / 10 \mathrm{d} \mathrm{B}=10^{3.7}=5.0 \times 10^{3} $$
Work Step by Step
First we use $$\Delta \beta_{12}=\beta_{1}-\beta_{2}=(10 \mathrm{dB}) \log \left(I_{1} / I_{2}\right)$$
Since $$\Delta \beta_{12}=(10 \mathrm{dB}) \log \left(I_{1} / I_{2}\right)=37 \mathrm{dB},$$ we get
$$
I_{1} / I_{2}=10^{37} \mathrm{dB} / 10 \mathrm{d} \mathrm{B}=10^{3.7}=5.0 \times 10^{3} $$
