Understanding if a logarithmic function is continuous or not

What is the definition of continuity in the context of the logarithmic function?

Explain the domain of the logarithmic function and its implications for continuity.

Describe the behavior of the logarithmic function as it approaches its vertical asymptote.

How does shifting the graph of the logarithmic function affect its continuity?

What common misconception do people have about asymptotes and continuity?