| ## 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(10 ^{n}) = nGood. ## 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 10^{2} 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 10^{8}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. |

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