Final answer:
The expression can be simplified using the properties of logarithms. Applying the power rule, we end up with log(6) + 4 * log(5+x) - 2 * log(x).
Step-by-step explanation:
The given expression is log((6(5+x)⁴)/(x²)). To simplify this expression, we can use the properties of logarithms. Firstly, we can rewrite the expression as: log(6) + log((5+x)⁴) - log(x²). Next, we can apply the power rule of logarithms, which states that log(aⁿ) = n * log(a). Using this rule, we simplify the expression further as: log(6) + 4 * log(5+x) - 2 * log(x).