$\ln\left({\left( y+9 \right)\sqrt[7]{{\left( y+9 \right)}^{4}}}\right)$
Use $\ln\left({x \times y}\right)=\ln\left({x}\right)+\ln\left({y}\right)$ to expand the expression$\ln\left({y+9}\right)+\ln\left({\sqrt[7]{{\left( y+9 \right)}^{4}}}\right)$
Write the expression in exponential form with the base of $y+9$$\ln\left({y+9}\right)+\ln\left({{\left( y+9 \right)}^{\frac{ 4 }{ 7 }}}\right)$
Use $\ln\left({{a}^{c}}\right)=c \times \ln\left({a}\right)$ to transform the expression$\ln\left({y+9}\right)+\frac{ 4 }{ 7 } \times \ln\left({y+9}\right)$
Calculate the sum$\frac{ 11 }{ 7 } \times \ln\left({y+9}\right)$