Final answer:
To expand the expression log4(w / (z * x)), we use the logarithmic properties that allow us to express division as subtraction and multiplication as addition of logs, resulting in log4 w - log4 z - log4 x.
Step-by-step explanation:
The question is asking for the correct way to expand a logarithmic expression using logarithmic properties. The relevant property for this question is that the logarithm of a division of two numbers can be expressed as the difference of their logarithms: Loga (x/y) = Loga x - Loga y. Thus, to expand the expression log4 (w / (z * x)), we use this property to separate the division and multiplication within the logarithm.
First, dealing with the division, we have log4 w - log4 (z * x) by the division rule. Then, addressing the multiplication within the remaining logarithm, we apply the property that states the logarithm of a product is the sum of the logarithms: Loga(xy) = log ax + logay. Therefore, log4 (z * x) becomes log4 z + log4 x. Putting it all together, the expression expands to log4 w - log4 z - log4 x.