by TheAxis October 26, 2008
Get the Logarithm mug.MATHEMATICS: The exponent, or power, to which 10 has to be raised to express any positive real number.
Logarithm is derived from Greek logos "reckoning, ratio," and arithmos "number."
Logarithm is derived from Greek logos "reckoning, ratio," and arithmos "number."
Since I can't make a nice table, let's use the following format: Base, Exponent, Expression, Result such that in line 1, Base = 10, Exponent = -3, Expression = 10^-3, Result = 0.001. We obtain,
10, -3,10^-3, 0.001 (or 1/1000) (line 1)
10, -2, 10^-2, 0.01 (or 1/100)
10, -1, 10^-1, 0.1 (or 1/10)
10, 0, 10^0, 1
10, 1, 10^1, 10
10, 2, 10^2, 100 (10 squared)
10, 3, 10^3, 1,000 (10 cubed)
And so forth.
Any positive real number can be expressed as the product of 10 raised to any real number; for example 100,000 can be written as 100 x 1000 = 10^2 x 10^3 = 10^5. Notice that the exponents are additive. It is easy to show that for division the exponents subtract.
Before the advent of hand-held electronic calculators, logarithms and the use of log tables reduced calculating time by converting long-hand multiplication into an addition process and long-hand division into a subtraction process where the result was accurate to three significant figures. One would just look up the logarithms of two or more numbers that were being multiplied, sum the logarithms, and then look up the corresponding number.
Another benefit of using logarithms is that curvilinear data points can be converted into linear data points, and the latter is easier to model with a first-order equation derived using either graph paper or linear regression analysis.
10, -3,10^-3, 0.001 (or 1/1000) (line 1)
10, -2, 10^-2, 0.01 (or 1/100)
10, -1, 10^-1, 0.1 (or 1/10)
10, 0, 10^0, 1
10, 1, 10^1, 10
10, 2, 10^2, 100 (10 squared)
10, 3, 10^3, 1,000 (10 cubed)
And so forth.
Any positive real number can be expressed as the product of 10 raised to any real number; for example 100,000 can be written as 100 x 1000 = 10^2 x 10^3 = 10^5. Notice that the exponents are additive. It is easy to show that for division the exponents subtract.
Before the advent of hand-held electronic calculators, logarithms and the use of log tables reduced calculating time by converting long-hand multiplication into an addition process and long-hand division into a subtraction process where the result was accurate to three significant figures. One would just look up the logarithms of two or more numbers that were being multiplied, sum the logarithms, and then look up the corresponding number.
Another benefit of using logarithms is that curvilinear data points can be converted into linear data points, and the latter is easier to model with a first-order equation derived using either graph paper or linear regression analysis.
by Nickelman from the boonies. April 4, 2013
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The most crappy (C-RRRR-AAAA-P-EEEE) subject in the world. Logarithms tell how many times a number x must be divided by the base b to get 1, and hence can be considered an inverse of exponentiation. Yeah, whatever!
Me: I have been trying to understand this logarithm crap with its shitty tables for the past seven weeks.
He: Yuck!
He: Yuck!
by WannaBeCow September 3, 2006
Get the Logarithm mug.When our primitive instinct makes us treat the comparison of large numbers as logarithmic rather than linear—for instance, we feel like the gap between a trillion and a billion is the same as that between a billion and a million, because both are a thousand times bigger, when the jump to a trillion is really much bigger.
When young children are asked which number is halfway between one and nine, their answers are three instead of five, as given by those with formal schooling. Is this a case of logarithmic instinct, where the middle is in relation to multiplication rather than addition: 1 × 3 = 3, 3 × 3 = 9?
by MathPlus October 8, 2020
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It's an important part of Calculus 1, used for taking the derivative of functions with "x" in the exponent.
It's an important part of Calculus 1, used for taking the derivative of functions with "x" in the exponent.
by Butts666 December 15, 2017
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it starts with l, like lame-o and loser, but it's actually a compliment!
it starts with l, like lame-o and loser, but it's actually a compliment!
by idk!? February 12, 2008
Get the logurithier mug.worse than anything known to man before. Based upon the multi-sexual origins of the universal constant: mathematics.
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