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

1 Answer
Jan 16, 2018

It's negative infinity.


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