Question

what is the domain of the function (y = 3 ln x) graphed below?

• (x > 0)
• (x < 0)
• (x < 3)

Explanation:

⚡ Using what you learned: domain and range · Understanding Logarithmic Functions

Step 1: Identify the domain condition for logarithmic functions

For any logarithmic function of the form \( y = a \ln(g(x)) \), the argument must be strictly greater than zero:

$$ g(x) > 0 $$

Step 2: Apply to the given function

For the function \( y = 3 \ln x \):

$$ x > 0 $$

This is also supported by the graph, which only exists to the right of the y-axis (\( x = 0 \)) and approaches the y-axis as a vertical asymptote.

Answer:

\( x > 0 \)