Solve d>aoperatorname{cog}_{10}9-log_{10}25+1

$$d > a \operatorname { cog } _ { 10 } 9 - \log _ { 10 } 25 + 1$$

Solve for o

$$\left\{\begin{matrix}o>\frac{\ln(2)d+\ln(5)d+\ln(\frac{5}{2})}{9\ln(10)acg_{10}}\text{, }&\left(a<0\text{ and }c<0\text{ and }g_{10}<0\right)\text{ or }\left(a<0\text{ and }c>0\text{ and }g_{10}>0\right)\text{ or }\left(a>0\text{ and }c>0\text{ and }g_{10}<0\right)\text{ or }\left(a>0\text{ and }c<0\text{ and }g_{10}>0\right)\\o\in \mathrm{R}\text{, }&d>-\frac{\ln(\frac{5}{2})}{\ln(10)}\text{ and }\left(g_{10}=0\text{ or }c=0\text{ or }a=0\right)\\o<\frac{\ln(2)d+\ln(5)d+\ln(\frac{5}{2})}{9\ln(10)acg_{10}}\text{, }&\left(a>0\text{ and }c<0\text{ and }g_{10}<0\right)\text{ or }\left(a>0\text{ and }c>0\text{ and }g_{10}>0\right)\text{ or }\left(a<0\text{ and }c>0\text{ and }g_{10}<0\right)\text{ or }\left(a<0\text{ and }c<0\text{ and }g_{10}>0\right)\end{matrix}\right.$$

Solve for g_10

$$\left\{\begin{matrix}g_{10}>\frac{\ln(2)d+\ln(5)d+\ln(\frac{5}{2})}{9\ln(10)aco}\text{, }&\left(a<0\text{ and }c<0\text{ and }o<0\right)\text{ or }\left(a<0\text{ and }c>0\text{ and }o>0\right)\text{ or }\left(a>0\text{ and }c>0\text{ and }o<0\right)\text{ or }\left(a>0\text{ and }c<0\text{ and }o>0\right)\\g_{10}\in \mathrm{R}\text{, }&d>-\frac{\ln(\frac{5}{2})}{\ln(10)}\text{ and }\left(o=0\text{ or }c=0\text{ or }a=0\right)\\g_{10}<\frac{\ln(2)d+\ln(5)d+\ln(\frac{5}{2})}{9\ln(10)aco}\text{, }&\left(a>0\text{ and }c<0\text{ and }o<0\right)\text{ or }\left(a>0\text{ and }c>0\text{ and }o>0\right)\text{ or }\left(a<0\text{ and }c>0\text{ and }o<0\right)\text{ or }\left(a<0\text{ and }c<0\text{ and }o>0\right)\end{matrix}\right.$$