Question

What is the limit of ln(x-7) as x approaches 7 from the right?

Answer 1

It's negative infinity.

Explanation:

If whatever's inside the natural logarithm approaches zero, that logarithm will approach negative infinity. To put it in stricter terms, we can set `u=x-7`, so then you'll have the limit of `ln(u)` as `u` approaches `0` from the right (it's not defined for negatives anyway) which we "know" is negative infinity (meaning it's written in the books, if a rigorous proof is needed, that's another story).

To put it into perspective intuitively as well, the natural logarithm of something is what you need to raise `e` (positive constant) to in order to get said something, and you'll need to raise it to really large negative powers to get something that gets close to zero

(`e^-n=1/(e^n)`)