Hate math? It turns out that a lot of us do!
I believe that is largely because we are not given an appreciation for it when we are young. Throughout our childhood and all of grade school, we are given problems and expected to solve them. Few teache...
When I last wrote about operations, I mentioned the shorthand of repeated multiplication, known as exponentiation. I also went on to mention its inverse, known as rooting, and briefly mentioned that the two are part of the larger topic of logarithms. Today, I would like to spend a bit more time explaining what these are and how we can apply them.
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If you like this, keep on reading...
A logarithm, or log for short, is an operator not unlike an exponential in that it takes two operands. The first is the base of the logarithm, which tells us what number we are planning to repeatedly divide by. The second is called the argument, which is the number we will be repeatedly dividing. In the example
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the base is 2 and the argument is 8. Put more verbosely, this logarithm is asking how many times we can divide our argument, 8, by our base, 2. From exponentiation, we know that 2^3 = 8 and hence the answer is 3. Because this reader lacks subscripts, I will be using a slightly different notation to express the above:
log_2(8) = 3
Before I move on, allow me to clarify what I mentioned last time regarding inverses. The inverse of an operation is its mathematical reverse. To reverse addition, we use subtraction; to reverse multiplication, we use division. The idea of an inverse is dependant upon which operand you would like to be able to calculate given an answer to your expression. This means that if we have two operands, we have two different inverses!
As we saw previously: When the power is kept constant, the inverse of exponentiation is rooting.
5^2 = 25 <=> sqrt(25) = 25^(1/2) = 5
Notice how the power remains 2 on both sides. The second notation that I introduced above is something I did not mention earlier: The n-th root of a number is the same thing as that number raised to the 1/n-th power. The square root of a number is then the same thing as that number raised to the power of a half.
