## anonymous 4 years ago how do i find the limit ln(x-3) x-->3+

1. TuringTest

it's approaching from the right, so it's defined because x-3 is positive and what number does lny approach as y approaches zero?

2. anonymous

ln 0 = infinity

3. TuringTest

...because x^a is always positive for x>0 we can only make it small by making 'a' large negative

4. anonymous

oh kinda get it

5. anonymous

you migth think of it like this. the log is the inverse of the exponential. when would $e^x=0$? well never, but it would be close to zero if x went to minus infinity

6. TuringTest

yes it should be minus^ Igb is a bit off

7. anonymous

so as x goes to minus infinity, $e^x$ goes to zero and as x goes to zero, $\ln(x)$ goes to minus infinity