I need help with a limit:

lim t-infinity [ln(t+1/t+2)-ln(1/2)]
My solution manual says you should end up with ln(1)-ln(2)=ln(2), however I dont know how they got to the ln(2).

Question

I need help with a limit:
 
lim t->infinity [ln(t+1/t+2)-ln(1/2)]  
My solution manual says you should end up with ln(1)-ln(2)=ln(2), however I dont know how they got to the ln(2).

anonymous · Answer

$$\lim_{t \rightarrow \infty} [\ln ((t+1)/(t+2))-\ln (1/2)]$$

zarkon · Answer

$$\frac{t+1}{t+2}\to 1\text{ as }t\to\infty$$
$$\ln(1)=0$$
$$-\ln(1/2)=\ln(2)$$

zarkon · Answer

$$-\ln\left(\frac{1}{2}\right)=\ln\left(\left(\frac{1}{2}\right)^{-1}\right)=\ln(2)$$

anonymous · Answer

Okay I get it now, that you Zarkon!