Simplify log_3(27) - log_3(9).

Step 1 (Method 1: Direct Evaluation): We can evaluate each logarithmic term individually:

• ${\log }_3(27)$: Since $27=3^3$, ${\log }_3(27)=3$.

• ${\log }_3(9)$: Since $9=3^2$, ${\log }_3(9)=2$.

Subtracting the two values:

Step 2 (Method 2: Quotient Rule): Using the logarithmic quotient property ${\log }_b(x)-{\log }_b(y)={\log }_b\left(\frac{x}{y}\right)$:

Step 3 (Conclusion): The simplified value is exactly 1.