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.
The 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……..