Question

write a rule for g that represents a vertical stretch by a factor of 6, followed by a translation 5 units down of the graph of $f(x)=log_{6}x$.
$g(x)=\square$

Explanation:

Step1: Apply vertical stretch by 6

Multiply $f(x)$ by 6:
$6f(x) = 6\log_{6}x$

Step2: Translate 5 units down

Subtract 5 from the stretched function:
$g(x) = 6\log_{6}x - 5$

Answer:

$g(x)=6\log_{6}x - 5$