To solve this problem, we need to identify how to translate the equation [tex]\( y = \ln(x) \)[/tex] five units down. A downward translation of a function can generally be represented by subtracting a constant from the function's output.
Given:
[tex]\[ y = \ln(x) \][/tex]
To translate this function five units down, we subtract 5 from the output of the function, resulting in:
[tex]\[ y = \ln(x) - 5 \][/tex]
Therefore, the equation that translates [tex]\( y = \ln(x) \)[/tex] five units down is:
[tex]\[ y = \ln(x) - 5 \][/tex]
So the correct answer is:
[tex]\[ y = \ln(x) - 5 \][/tex]
