1/8 Vs. 1/4 ( 1/8 LARGER than 1/4 )

1/8 Vs. 1/4 (1/8 LARGER than 1/4)

Can anyone can tell me which is greater among 1/4 and 1/8 ? Normally we will answer this question with 1/4 . Lets make a difference in this . I say 1/8 is larger than 1/4 . Let me Prove 1/8 is larger than 1/4 .

We Know that ,

3 > 2   
3 log(1/2) > 2 log(1/2)    // Multiply log (1/2) on both sides ..( log means log base 10 )
log[(1/2)³] > log[(1/2)²]  // Property of logrithms
(1/2)³ > (1/2)²   // Take anti-log on both sides
1/8 > 1/4

Here is my solution to prove something not possible . Can you find the fallacy I have used in this Proof ? 

Ans :  The Answer is that the multiplication of log(1/2) in the second step is the fallacy . In reality , log(1/2) is a negative value .