Verify if limit of ln(1+x)/x is 1, x-->0

In other words, we'll have to prove
that:

lim [ln(1+x)]/x =
1

We'll re-write the
function:

lim (1/x)*ln(1+x) =
1

We'll apply the power property of
logarithms:

lim  ln [(1+x)^(1/x)] = ln lim
[(1+x)^(1/x)]

But, for x->0 lim [(1+x)^(1/x)] = e
(remarcable limit)

lim  ln [(1+x)^(1/x)] = ln
e

We know that ln e =
1

So, for x->0, lim  ln [(1+x)^(1/x)]
= 1.