Answer
The equivalent expression for ${{\log }_{a}}{{x}^{4}}{{y}^{2}}{{z}^{3}}$is $4{{\log }_{a}}x+2{{\log }_{a}}y+3{{\log }_{a}}z$.
Work Step by Step
${{\log }_{a}}{{x}^{4}}{{y}^{2}}{{z}^{3}}$
Evaluate the expression in terms of a sum as follows.
Apply the product rule for logarithms.
${{\log }_{a}}{{x}^{4}}{{y}^{2}}{{z}^{3}}={{\log }_{a}}{{x}^{4}}+{{\log }_{a}}{{y}^{2}}+{{\log }_{a}}{{z}^{3}}$
Apply the power rule for logarithms.
${{\log }_{a}}{{x}^{4}}{{y}^{2}}{{z}^{3}}=4{{\log }_{a}}x+2{{\log }_{a}}y+3{{\log }_{a}}z$
