Question

condense log expression
ln x + 9 ln y

Explanation:

Step1: Apply power rule of logs

The power rule of logarithms states that \( n\ln a=\ln(a^n) \). For \( 9\ln y \), we apply this rule: \( 9\ln y = \ln(y^9) \).

Step2: Apply product rule of logs

The product rule of logarithms states that \( \ln a+\ln b = \ln(ab) \). Now we have \( \ln x+\ln(y^9) \), applying the product rule gives \( \ln(xy^9) \).

Answer:

\(\ln(xy^9)\)