How can we calculate the logarithms by hand without using any calculator?
Here is how to calculate logarithms by hand using only multiplication and subtraction.And this procedure produces digit by digit, so you can stop whenever you have enough digits.Before we do that, let’s give an example so it will be easier to understand:Log 2 = 0,30103…If we take the 10th power:log (2^10) = 10 X 0,30103… = 3.0103…then the digits in the logarithm have all shifted 1 place to the left.But also: 2^10 = 1024We can see that the log of 1024 must be 3 point something because 1024 is slightly over 1000.If we can find the 10th power on a normal calculator we know he first digit of the logarithm by looking at the number before the decimal point:0-9 => 010-99 => 1100-999 => 21000-9999 => 3etc.So log 1024 is 3.????. We have retrieved the first digit of log 2.If we subtract 3 from this number we can go through the previous procedure again to retrieve the next number.The 10th power is easily calculated on paper by multiplying a number by itself 3 times:2 X 2 =44 X 4 = 1616 X 16 = 256And the multiplying 256 with the result of the first calculation: 4256 X 4 = 1024So 4 multiplications in total.I divide 1024 by 1000 to get 1.024Doing the same procedure I get:1.2676506So the next digit is 0.And then taking 1.2676506 through this procedure I get:10.715806So the next digit is 1.I divide 10.715806 by 10 to get 1.0715806And then taking 1.0715806 through this procedure I get:1.995063So the next digit is 0.And then taking 1.995063 through this procedure I get:999.00506So the next digit is 2.However since it is so close to 1000 we can round the digit to 3.Now we have 3.0103
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Has a policing culture of "shooting first and asking questions later" when the officer feels threatened displaced the obligation for law enforcement to investigate and uncover the truth and facts of situations to which they are called to respond?
No.I was not present for the Sacramento shooting and thus do not know what, from the totality of circumstances that were presented, just what indicated to the officer that firing their gun was a good idea. Were you present? Did the man so tragically killed hold his cell phone so that it appeared to be a gun? I don’t know.Your premise makes no sense as it presumes that all officers shoot whenever they feel threatened. It is so far removed from reality that it would be hilarious if it’s implications weren’t so tragic. Seriously, we would have a lot of dead bodies if it were true. Your premise overlooks the fact that hundreds if not more officers feel threatened on a daily basis but use their training to defuse the situation without having to shoot anyone. Virtually every officer-involved shooting is reviewed by the officer’s department to see if it was within policy. Many are reviewed again in the context of a civil lawsuit against the department. An officer who developed a reputation for “cowboying it up” in these situations will also develop a reputation for riding a desk or for being unemployed as a result.