The Puzzle:

How can I get the answer 24 by only using the numbers 8,8,3,3.

You can use add, subtract, multiply, divide, and parentheses.

Bonus rules: also allowed are logarithms, factorials and roots

Our Solution:

1) Supplied by "mathsyperson":
8/(3-(8/3))
= 8/(1/3)
= 24

2) Supplied by "puzzler09" (using bonus rules):
((8 x 3!)/3)+8
= ((8 × 3 × 2 × 1)/3)+8
= (48/3)+8
= (16)+8
= 24

3) Supplied by "Mark" (using bonus rules):
(3!/ )*8

4) Supplied by "Daryl S" (using bonus rules):
(8-3)!/(8-3)
(  ×  )!
(  +  )!
√(8×8×3×3)
8+(8×(3!/3))
((√(8+8) × (3/3))!
√(8+8) × (3+3)
(log base(3!/3) of 8) × 8
((log base(3!/3) of (8+8))!