​Solve each equation for the exact value of $x$.  

1. $\ln(x)=3$ 

   Step (a):

   $e^3=x$

2. $e^x=200$ 

   Step (b):

   $\ln(e^x)=\ln(200)$

3. $5\ln(x+1)=20$ 

   Step (c):

   $\ln(x+1)=4$

4. $e^{(x+2)}+20=100$ 

   Step (d):

   $e^{(x+2)}=80$