Use the properties of logarithms to condense $6{\log }_{10}(x+y)+4{\log }_{10}w$ .

A) ${\log }_{10}{x}^6{y}^6{w}^4$
B) ${\log }_{10}\left(x^6+y^6\right)w^4$
C) ${\log }_{10}(6(x+y)+4w)$
D) ${\log }_{10}24(x+y)w$
E) ${\log }_{10}(x+y{)}^6{w}^4$

Using the property that states that the sum of logarithms is equivalent to the logarithm of the product, we can rewrite the expression as:

$$6{\log }_{10}(x+y)+4{\log }_{10}w={\log }_{10}(x+y{)}^6+{\log }_{10}{w}^4$$

Then, using the property that states that the logarithm of a product is equivalent to the sum of logarithms, we can condense the expression as:

$${\log }_{10}(x+y{)}^6+{\log }_{10}{w}^4={\log }_{10}(x+y{)}^6{w}^4$$

This matches answer choice E, so the best choice is E.