Limits of x/ln(x): Solving Confusion

[masterchiefo]

Homework Statement

Hello all,

I am having hard time with limits.

1. lim_x->1^- x/ln(x)

2. lim_x->1⁺ x/ln(x)

Homework Equations

The Attempt at a Solution

1. lim_x->1^- x/ln(x)
= 1^-/ln(1^-)
ln(1-) = 0^-

I seriously don't understand why ln(1-) = 0-

2. lim_x->1⁺ x/ln(x)
= 1⁺/ln(1⁺)
ln(1+) = 0⁺

I seriously don't understand why ln(1+) = 0+thanks

 

[axmls]

Do you know what the natural logarithm graph looks like?

 

[masterchiefo]

Do you know what the natural logarithm graph looks like?

yes I do, doing limits with a graph is easy, I have to resolve this by doing algebra.

 

[axmls]

You say you don't understand why ln(1) = 0. This is common knowledge about the logarithmic function. You have a function approaching 0 in the denominator and a function approaching 1 in the numerator. What does that tell you?