Yep, you’ve read that right.

Here we go (log below means log10, so log with base 10):

3 > 2

3 log(1/2) > 2 log(1/2)

log[(1/2)³] > log[(1/2)²]

(1/2)³ > (1/2)²

1/8 > 1/4

3 log(1/2) > 2 log(1/2)

log[(1/2)³] > log[(1/2)²]

(1/2)³ > (1/2)²

1/8 > 1/4

Convinced? If not, what’s wrong with the proof above?

In reality log10(1/2) is negative, so the second step of the proof is not valid.

Credit: I saw the above trick on a lesson by prof. Arnaldo Viera Moura at Unicamp.

Ali AsgharThe proof is wrong because multiplying both sides by log(1/2) is exactly like multiplying by a negative number so it reverses the relation sign……..