How does 1 equal 3?

Answer 1

There was a spurious "proof" that uses exponentials, notably the fact that (-1) cubed (or raised to any odd power) is still equal to -1.
(-1)(-1)(-1) = -1
Since you can represent an exponential value x^n as n(log x), you convert the two sides to log values and then divide by x, which here is (log -1):
(-1) = (-1)^3
(-1)^1 = (-1)^3
1 (log -1) = 3 (log -1)
1 = 3

Of course, the fallacy is that it is the identity property of 1 that allows the first equation, so it cannot be extended as other numbers might be.