Math question, loosely related to python... The python "Think Like a Computer Scientist" pdf tutorial assumes you have a familiarity with logarithmic equations and whatever sin stands for (will look into that next). I never learned this stuff. I understand some of the basic mechanics here, like that a log is sort of a reverse exponent. I can do a simple equation like finding the log of 36 with a base of 6. But I don't get why the logarithm of 1 is always equal to 0

Question

Math question, loosely related to python...             The python "Think Like a Computer Scientist" pdf tutorial assumes you have a familiarity with logarithmic equations and whatever sin stands for (will look into that next). I never learned this stuff. I understand some of the basic mechanics here, like that a log is sort of a reverse exponent. I can do a simple equation like finding the log of 36 with a base of 6. But I don't get why the logarithm of 1 is always equal to 0

anonymous · Answer

Heres an example problem

   Evaluate  log1 with a base of 8.

    8 to what exponent produces 1?  0 with a base of 8 = 1.

log1 with a base of 8 = 0.

We can observe that, in any base, the logarithm of 1 is 0.
so: 

log1 with base of b = 0

anonymous · Answer

why is the log of 1 with a base of 8 equal to 0 rather than 1/8 ??
How does that make sense?

anonymous · Answer

(8 *1) /8 = 1/8 or  0.125 so 0.125 * 8 = 1
Didn't I just equate the logarithm of 1 with a base of 8??

anonymous · Answer

Hi Evil - this is something I had real problems remembering, so I had to check for myself before the light came on again!

I think of logs exactly as the reverse of exponents - it's the only way it makes sense to me, and by doing an exponent first, you can make your own language for the logs

e.g. exp 8 (3) is just "8 raised to the power of 3" --- log 8 (3) to me can be rephrased as "8 to the power of what number will give you 3?"

When I think of it like that, then exp (0) in any base is a number to the power of zero, and that always gives you the answer of one. Doing this in reverse (i.e. log(1) ) should always result in zero. "(base) to the power of what number will give you 1?"

I really hope this isn't even more confusing!!

anonymous · Answer

Kahn academy has a great video on log http://www.youtube.com/watch?feature=player_embedded&v=mQTWzLpCcW0

anonymous · Answer

Any number to the power of 0 is 1. That's what was throwing me off. It would seem that it doesn't make sense, that rather a number to the power of nothing would naturally be nothing, but that apparently isn't the case. Next I've got to find out why (but that's a problem for a math forum - as was this one, really)... Thank you both for your help!