Solve: (1/2)log₃9 - log₃1.5 Logarithmic Expression

$\frac{1}{2}\log_39-\log_31.5=$

To solve the problem $\frac{1}{2}\log_39-\log_31.5$, we need to apply the rules of logarithms:

• **Step 1: Simplify with the power rule**
  Using the power rule $\frac{1}{2}\log_39 = \log_39^{1/2}$. Since $9 = 3^2$, we have $9^{1/2} = 3^{2 \cdot 1/2} = 3^1$. Thus, $\frac{1}{2}\log_39 = \log_3 3 = 1$.
• **Step 2: Apply the subtraction rule**
  Now, the expression becomes $1 - \log_3 1.5$. Using the subtraction rule: $1 - \log_3 1.5 = \log_3 3 - \log_3 1.5 = \log_3 \left(\frac{3}{1.5}\right)$.
• **Step 3: Simplify the fraction**
  Calculate $\frac{3}{1.5}$: it simplifies to 2 because $3 \div 1.5 = 2$.

Thus, the simplified expression is $\log_3 2$.

Using the provided answer choices, the correct answer matches choice $\log_3 2$, which corresponds to choice 2.

Therefore, the solution to the problem is $\log_3 2$.