Afolayan, let's knock this out. Step 1: Apply the power rule of logarithms, $a \log b = \log b^a$, to each term. $$ \frac{1}{2}\log 25 = \log 25^{1/2} = \log \sqrt{25} = \log 5 $$ $$ 2\log 3 = \log 3^2 = \log 9 $$ $$ 2\log 6 = \log 6^2 = \log 36 $$ Step 2: Substitute these simplified terms back into the original expression. $$ \log 5 - \log 9 + \log 36 $$ Step 3: Apply the subtraction rule of logarithms, $\log a - \log b = \log \left(\frac{a}{b}\right)$. $$ \log 5 - \log 9 = \log \left(\frac{5}{9}\right) $$ Step 4: Apply the addition rule of logarithms, $\log a + \log b = \log (a \cdot b)$. $$ \log \left(\frac{5}{9}\right) + \log 36 = \log \left(\frac{5}{9} \times 36\right) $$ Step 5: Simplify the expression inside the logarithm. $$ \frac{5}{9} \times 36 = 5 \times \frac{36}{9} = 5 \times 4 = 20 $$ Step 6: Write the final simplified expression. $$ \log 20 $$ The simplified expression is: $$\boxed{\mathbf{\log 20}}$$ What's next?