suprisingly busy

i know i know.. one week no update..

found out surprisingly that even i can be busy lol.. especially when you got 30+ games to play, mythbusters to watch everyday at 5pm on discovery, chase the anime "ah my goddess", learn fourier series, train your voice and on top of that, cook dinner every night. which is the worst i think.. (people who cook would understand..) But i managed to find some time to blog.. About maths again lol..

i came up with this in secondary three.. Mr Sin incorrectly dismissed it by stating that one equation cannot have two variables for it to be solved.. can you tell whats wrong with it?

we start with the equation,
a^x = -1

squaring both sides we would get...
a^(2x) = 1

since a is not zero and anything other than zero, to the power of zero is equal to one we have;

a^2x = a^ 0

and so,

2x = 0
x = 0

substituting this result into our original equation which was a^x = -1
we would get

a^0 = -1
1 = -1

which is of course impossible, but can you see where the error lies?