Estimate the solution to each of these equations without a calculator and justify your estimate. Then solve them to the nearest $0.001$.  

1.  $20^x=316$ 

   Hint (a):

   Since $20^2=400$, $x$ must be less than $2$.

2.  $7.3^x=4.81$ 

   Hint (b):

   $7.3^1=7.3$, so $x$ must be less than $1$.

3.  $160(0.5)^x=8$ 

   Step (c):

   $\left(\frac{1}{2}\right)^x=\frac{8}{160}=\frac{1}{20}$

   More Help (c):

   $\left(\frac{1}{2}\right)^4=\frac{1}{16}$