To determine the domain of the function [tex]\( y = \log_5 x \)[/tex], we need to understand the properties of the logarithmic function. A logarithm [tex]\( \log_b (x) \)[/tex] (where [tex]\( b \)[/tex] is the base and [tex]\( x \)[/tex] is the argument) is defined only for positive real numbers. This means that the argument [tex]\( x \)[/tex] of the logarithmic function must be greater than 0.
Let's summarize the key points:
1. Logarithmic Function Properties: The logarithm is defined only for positive values of the argument. Therefore, [tex]\( x \)[/tex] must be greater than 0.
2. Implication for the Domain: Since [tex]\( y = \log_5 x \)[/tex] requires [tex]\( x \)[/tex] to be positive, the domain of this function is all real numbers greater than 0.
Based on these points, the correct answer is:
- all real numbers greater than 0.
