Question

what is the limit of x->1 of In(x)?

Answer 1

I believe ln is continuous for x > 0, so this will be the same as asking what is ln(1).

\(\ln x\) is the same as \(\log_e x\)

Answer 2

We know that:

\(\log_a b = c\) means \(a^c = b\).

Answer 3

So, we're asking what is \(\ln 1\), meaning:

\[\log_e 1 = x\]
We can move this around:

\[e^x = 1\]
And the answer to that is x = 0, since raising any number to 0 gives you 1.

Answer 4

okay. thank you

Answer 5

Thus, \[\lim_{x \rightarrow 1} \ln x =0\]

Answer 6

No problem!