Question

condense log expression
ln x + 9ln y
a. ln xy⁹
b. ln (x + 9y)
c. none

Explanation:

Step1: Apply Power Rule of Logarithms

The power rule states that \( a\ln b=\ln(b^a) \). For \( 9\ln y \), we get \( \ln(y^9) \).

Step2: Apply Product Rule of Logarithms

The product rule states that \( \ln a+\ln b = \ln(ab) \). Now, \( \ln x+\ln(y^9)=\ln(xy^9) \) (which can also be written as \( \ln xy^9 \) as in option A).

Answer:

A. \( \ln xy^9 \)