I get 4 scores and I need to sort them from most relevant(biggest score) to the least.
1)$$\frac{3}{9}\log(\frac{1}{4})$$
2)$$\frac{3}{12}\log(\frac{1}{4})$$
3)$$\frac{3}{8}\log(\frac{1}{4})+\frac{1}{8}\log(\frac{1}{3})$$
4)$$\frac{3}{7}\log(\frac{1}{4})$$
5)$$\frac{1}{5}\log(\frac{1}{3})+\frac{1}{5}\log(\frac{1}{4})$$
I get these 5 scores and I need to sort them.This is a derived problem from Computer Science, but because the mathematical aspect, I post it here.
The base of the log is not critical(however after choosing a certain base it needs to remain constant throughout the 5 scores).
I can tell that 1 is more relevant than 2 because log part is the same and the difference between coefficients. The same goes for the fourth score. However I can't manage to find a way to determine which of the others stands compared to the results I already have.
I know this is subjective, but I need to find a preferable(the quicker the better) way to estimate the results.
Since you can choose any base for log, use base 4. Then $\log_4(1/4)=-1$. Then we know that $1/4<1/3<1/2$, so $\log_4(1/4)<\log_4(1/3)<\log_4(1/2)$ or $-1<\log_4(1/3)<-0.5$. Can you take it from here?