Question

identify the equation that translates ( y = ln(x) ) five units down.
( y=ln(x - 5) )
( y=ln(x)+5 )
( y=ln(x + 5) )
( y=ln(x)-5 )

Explanation:

Step1: Recall vertical translation rule

For a function \(y = f(x)\), translating it \(k\) units down gives \(y=f(x)-k\).

Step2: Apply the rule to \(y = \ln(x)\)

Here \(k = 5\), so the translated function is \(y=\ln(x)-5\).

Answer:

\(y=\ln(x)-5\) (the fourth option)