Without using a calculator, find the solution to each equation. 

1. $2^x = 17$ 

   Hint (a):

   Start by taking the log of both sides.

   Answer (a):

   $x=\frac{\text{log}17}{\text{log}2}$

2. $\log_3(x+1)=5$ 

   Answer (b):

   $x = 242$

3. $\log_3(3^x)=4$ 

   Answer (c):

   $x = 4$

4. $4^{\log_4(x)}=7$ 

   Answer (d):

   $x = 7$