Take the natural logarithm (ln) of both sides of the equation.

$$x = \frac{\ln 3}{2 \ln 3 - \ln 5}$$

Using logarithm properties, $2 \ln 3 = \ln(3^2) = \ln 9$.

$$x = \frac{\ln 3}{\ln 9 - \ln 5}$$ $$x = \frac{\ln 3}{\ln \left(\frac{9}{5}\right)}$$

Calculate the numerical value:

$$x \approx \frac{1.0986}{2.1972 - 1.6094}$$ $$x \approx \frac{1.0986}{0.5878}$$ $$x \approx 1.869$$

The value of $x$ for science Vs library blocks is $\boxed{\mathbf{\frac{\ln 3}{\ln \left(\frac{9}{5}\right)} \approx 1.869}}$.

$$x = \frac{-(\ln 9 + 2 \ln 7)}{4 \ln 7 - 3 \ln 9}$$

Using logarithm properties, $2 \ln 7 = \ln(7^2) = \ln 49$ and $4 \ln 7 = \ln(7^4) = \ln 2401$ and $3 \ln 9 = \ln(9^3) = \ln 729$.

$$x = \frac{-(\ln 9 + \ln 49)}{\ln 2401 - \ln 729}$$ $$x = \frac{- \ln(9 \times 49)}{\ln \left(\frac{2401}{729}\right)}$$ $$x = \frac{- \ln(441)}{\ln \left(\frac{2401}{729}\right)}$$

Calculate the numerical value:

$$x \approx \frac{-(2.1972 + 2 \times 1.9459)}{4 \times 1.9459 - 3 \times 2.1972}$$ $$x \approx \frac{-(2.1972 + 3.8918)}{7.7836 - 6.5916}$$ $$x \approx \frac{-6.089}{1.192}$$ $$x \approx -5.108$$

The value of $x$ for sports Vs agricultural plots is $\boxed{\mathbf{\frac{- \ln(441)}{\ln \left(\frac{2401}{729}\right)} \approx -5.108}}$.