Final answer:
The translation from f(x) = log₅(x) to g(x) = log₅(x-2) is described as a horizontal shift of the graph of f(x) to the right by 2 units. This translation does not change the vertical position or the shape of the original graph.
Step-by-step explanation:
The statement that best describes the translation from f(x) = log₅(x) to g(x) = log₅(x-2) is that the graph of g(x) is the graph of f(x) shifted to the right by 2 units. This horizontal shift is due to the subtraction inside the logarithm function, indicating that the input value x must be larger by 2 to yield the same log value as f(x). It's important to note that this transformation does not affect the vertical position or the shape of the graph, only the horizontal placement.
Moreover, the property of logarithms that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers is not directly relevant to this translation. However, this property, along with others, is crucial for understanding the behavior of logarithmic functions in general. In this context, the subtraction of 2 within the logarithm (g(x) = log₅(x-2)) can be thought of as influencing when the logarithm will reach particular values, as opposed to altering the values themselves, as division would.