Answer
$\ln\sqrt[4] {x^3(x^2+3)}=\frac{3\ln~x}{4}+\frac{\ln(x^2+3)}{4}$
Work Step by Step
$\ln\sqrt[4] {x^3(x^2+3)}=\ln [x^3(x^2+3)]^{\frac{1}{4}}=\frac{1}{4}\ln [x^3(x^2+3)]=\frac{1}{4}[\ln~x^3+\ln(x^2+3)]=\frac{1}{4}[3\ln~x+\ln(x^2+3)]=\frac{3\ln~x}{4}+\frac{\ln(x^2+3)}{4}$
