Why is the log of 0 equal to -infinity why not infinity?

Answer 1

First let's say log100=x

If we rearrange this into exponential form, we get 10x=0

Now we know that a number to ANY exponent will NEVER give 0, it's mathematically impossible, unless you start dealing with infinities.

If we put in infinity for "x", we have 10infinity=0, however, we know this can't be possible, because if 10 is to the power of a positive number (even if it is infinitely small ("x" will just keep getting closer to 0 which will make the answer equal 1, and that's the absolute lowest number you can have with a positive exponent)) then it will never come close to 0.

Instead, if we have 10-infinity=0 we understand that the number becomes infinitely small (closer and closer to 0). Although it never technically reaches 0, it becomes so small that it is negligible. This idea is the same as a limit in calculus.