Questions: Write the expression as a logarithm of a single expression. [ 7 ln x-frac13 ln y ] [ 7 ln x-frac13 ln y= ]

Solution Steps

The logarithm power rule states that \( a \ln b = \ln b^a \). Apply this rule to both terms in the expression: \[ 7 \ln x = \ln x^7 \] \[ \frac{1}{3} \ln y = \ln y^{1/3} \]

The logarithm subtraction rule states that \( \ln a - \ln b = \ln \left( \frac{a}{b} \right) \). Apply this rule to the expression: \[ 7 \ln x - \frac{1}{3} \ln y = \ln x^7 - \ln y^{1/3} = \ln \left( \frac{x^7}{y^{1/3}} \right) \]

Final Answer