Can the following two equations be satisfied simulateously for $g,r>0$?
$$g^4r\left(5g-4\right)\geq\ln\left(2\right)\ $$
$$g^3r\left(4g-3\right)\leq\ln\left(1.25\right)$$
From eq.2, $$g^3r \leq \frac{ln(1.25)}{4g-3}$$
Then, $$g\big(\frac{ln(1.25)}{4g-3}\big)\left(5g-4\right)>\ln\left(2\right)\ $$
$$\iff \frac{g(5g-4)}{4g-3}>\frac{ln(2)}{ln(1.5)}$$
But not sure how to find values for $g$ and $r$. Any ideas?