Final answer:
To expand the expression (log₅(y)/(4z)), it is converted into a subtraction of logarithms, resulting in log₅(y) - log₅(4z), utilizing the logarithmic property that allows a division inside the logarithm to be expressed as subtraction.
Step-by-step explanation:
To expand the expression (log₅(y)/(4z)), we can apply the properties of logarithms. Since there is a division inside the logarithm, we can use the property that allows a quotient to be expressed as the subtraction of two logarithms. Therefore, the expanded form of this expression using the properties of logarithms is:
log₅(y) - log₅(4z)
Further expansion can occur if necessary by using other logarithmic properties such as the logarithm of a product — log(ab) = log(a) + log(b). However, given that this question does not request further expansion, we'll stop at the subtraction expression.