[tex]log_43+\frac{1}{3}log_45+\frac{1}{3}log_47[/tex]
start by using the property of the logarithm that states
[tex]n\ast log_ab=log_a(b^n)[/tex]
then, if we apply the property
[tex]log_43+log_4(5^{\frac{1}{3}})+log_4(7^{\frac{1}{3}})[/tex]
since all logarithms have the same base we can apply the property
[tex]log_a(b)+log_a(c)=log_a(b\ast c)[/tex]
apply the property
[tex]log_4(3\ast5^{\frac{1}{3}}\ast7^{\frac{1}{3}})[/tex]
simplify the product and write the potency as a radical
[tex]\begin{gathered} log_4(3\sqrt[3]{7\ast5}) \\ log_4(3\sqrt[3]{35}) \end{gathered}[/tex]
