To determine the domain of the function [tex]\( y = \log_5 x \)[/tex], we need to examine where the logarithmic function is defined.
1. The logarithmic function [tex]\( \log_b x \)[/tex] (where [tex]\( b \)[/tex] is the base) is defined only for positive values of [tex]\( x \)[/tex]. This is because we cannot take the logarithm of a negative number or zero in the realm of real numbers.
2. Thus, for the function [tex]\( \log_5 x \)[/tex], the argument [tex]\( x \)[/tex] must be greater than 0.
3. Therefore, the domain of [tex]\( y = \log_5 x \)[/tex] is all real numbers greater than 0.
So, the correct answer is:
- all real numbers greater than 0
