Use the properties of logarithms to condense the following expression as much as possible. writing the answer as a single term with a coefficient o All exponents should be positive. \[ \ln (4)+3 \ln (x)-3 \ln (y) \]

To condense the expression \(\ln (4)+3 \ln (x)-3 \ln (y)\), we can apply the properties of logarithms. First, recall that \(a \ln(b) = \ln(b^a)\) and \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\). Using these properties, we can rewrite the expression as follows: 1. Rewrite \(3 \ln (x)\) as \(\ln(x^3)\) and \(3 \ln (y)\) as \(\ln(y^3)\). 2. Therefore, the expression becomes: \[ \ln (4) + \ln (x^3) - \ln (y^3) \] 3. This can be combined as: \[ \ln\left(4 \cdot x^3\right) - \ln(y^3) \] 4. Finally, using the subtraction property of logarithms: \[ \ln\left(\frac{4 \cdot x^3}{y^3}\right) \] Thus, the condensed form of the given expression is: \[ \ln\left(\frac{4x^3}{y^3}\right) \]