Amit Assiznment: O Pause Precala lus Revilw Practice-Not Graded Question 7 - of 10 step 1 of 1 Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1. All exponents should be positive. \[ \ln (15)+9 \ln (x)-6 \ln (y) \]

To condense the expression \(\ln (15) + 9 \ln (x) - 6 \ln (y)\), we can use the properties of logarithms. First, remember that \(k \ln(a) = \ln(a^k)\) and the properties of addition and subtraction: \(\ln(a) + \ln(b) = \ln(ab)\) and \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\). Applying these properties, we rewrite your expression step-by-step: 1. Convert \(9 \ln(x)\) into \(\ln(x^9)\). 2. Convert \(-6 \ln(y)\) into \(-\ln(y^6)\). 3. Now combine: \[ \ln(15) + \ln(x^9) - \ln(y^6) = \ln(15) + \ln\left(\frac{x^9}{y^6}\right) \] 4. Finally, use the addition property: \[ \ln\left(15 \cdot \frac{x^9}{y^6}\right) \] 5. This results in: \[ \ln\left(\frac{15 x^9}{y^6}\right) \] So, the condensed expression is \(\ln\left(\frac{15 x^9}{y^6}\right)\).