Solve m_{0}-5/2logfrac{I_{2}}{I_{0}}=2m_{0}-5logfrac{I_{1}}{I_{0}}

$$m _ { 0 } - \frac { 5 } { 2 } \log \frac { I _ { 2 } } { I _ { 0 } } = 2 m _ { 0 } - 5 \log \frac { I _ { 1 } } { I _ { 0 } }$$

Solve for I_0

$$I_{0}=\frac{I_{1}^{2}\times 10^{-\frac{2m_{0}}{5}}}{I_{2}}$$

$$\left(I_{2}>0\text{ and }I_{1}>0\right)\text{ or }\left(I_{2}<0\text{ and }I_{1}<0\right)$$

Solve for I_1

$$I_{1}=\sqrt{\frac{I_{2}}{I_{0}}}I_{0}\times 10^{\frac{m_{0}}{5}}$$

$$\left(I_{2}<0\text{ and }I_{0}<0\right)\text{ or }\left(I_{2}>0\text{ and }I_{0}>0\right)$$