Use the properties of logarithms to expand the expression ${\log }_4\left[x^5(x+6{)}^2\right]$ . (Assume $x>0$ ) .

A) $5{\log }_{4}x+2{\log }_4(x+6)$
B) $5{\log }_{4}x\times 2{\log }_4(x+6)$
C) $\frac{{\log }_4{x}^5}{{\log }_4(x+6{)}^2}$
D) $5{\log }_{4}x+{\log }_4(x+6)$
E) $\left(5{\log }_{4}x\right)\times \left(2{\log }_{4}x\right)+2{\log }_{4}6x$

The expression ${\log }_4\left[x^5(x+6{)}^2\right]$ can be expanded using the properties of logarithms as follows: the logarithm of a product is the sum of the logarithms ( ${\log }_b(mn)={\log }_b(m)+{\log }_b(n)$ ), and the logarithm of a power is the exponent times the logarithm ( ${\log }_b(m^n)=n{\log }_b(m)$ ). Therefore, the expression expands to $5{\log }_{4}x+2{\log }_4(x+6)$ .