Don't worry, I'm not selling anything. Just giving a shoutout to one of my open-source side projects:
I created a programming language for beginners and am looking for people to test it out. If you have a spare moment (particularly if you haven't programmed before) and you're interested in making 2D games, please check it out.
Calculating Base 10 Logarithms in your HeadCalculating base 10 logarithms in your head on the fly is a lot easier than you may think. It is simply a matter of memorization and a little estimation...
First memorize all the single digit base 10 logs. Don't worry, it's not as painful as it sounds. I even made the chart for you:
Remember this rule from high school?
log(a*b) = log a + log b
And what about this one, you remember it too?
log(10n) = n
Example #1: base 10 log of 400That's the same thing as log(4*100) which equals log 4 + log 100. log of 4 you know from the table above. Log of 100 is log of 102 and therefore is equal to 2. So the log of 400 is 2 + log 4 which is 2.602. It might sound like a tedious method but try a few examples first and you will see it's actually pretty quick.
Now you may ask, what if it isn't just a number with a bunch of 0's after it?
Example #2: base 10 log of 35Suppose you wanted to find the logarithm of 35. This is the same thing as log(3.5 * 10). The log of 3.5 is somewhere between the log of 3 and 4, but somewhat above the midpoint (since the log scale gets smaller as you go up). Log of 3 is .477 and log of 4 is .602 so we'll make a rough guess around .54 or .55 ish. Log of 10 is obviously 1, so our guesstimate for the log of 35 will be 1 + 0.545.
Our guess: 1.545
Calculator says: 1.544068...
Now you can convince all your friends and teachers that you are a robot.
Example #3: base 10 log of 290438572:This is fairly close to log(2.9 * 100000000) = log 2.9 + log 108
2.9 is close to 3. Log(3) = .477, so we'll guess something slightly below that like .45
Our Guess: 8 + .45 = 8.45
Calculated Answer: 8.46305...
Now run off and scare some people with your new powers.