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May 14, 2018 · Exponents are supercript numerals that let you know how many times you should multiply a number by itself. Some real world applications include understanding scientific scales like the pH scale or the Richter scale, using scientific notation to write very large or very small numbers and taking measurements.
Exponents are simply a shorthand notation for multiplying the same number by itself several times – and in everyday life you just don't often need that, because it doesn't occur that often that you'd need to calculate 7 × 7 × 7 × 7 (which is 7 4) or 0.1 × 0.1 × 0.1 × 0.1 × 0.1 (which is 0.1 5) or other such calculations.
The exponent of a number says how many times to use the number in a multiplication. In 82 the "2" says to use 8 twice in a multiplication, so 82 = 8 × 8 = 64. In words: 8 2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared". Some more examples: Example: 53 = 5 × 5 × 5 = 125. In words: 5 3 could be called "5 ...
In real life, we use the concept of exponents to write numbers in a simplified manner and in a short way. Repeated multiplication can be easily written with the help of exponents. Also, we use exponents to write larger numbers, for example, the distance of the moon from earth, the number of bacteria present on a surface, etc.
- What Is A logarithm?
- Working Together
- The Natural Logarithm and Natural Exponential Functions
- The Common Logarithm
- Changing The Base
A Logarithmgoes the other way. It asks the question "what exponent produced this?": And answers it like this: In that example: 1. The Exponent takes 2 and 3 and gives 8 (2, used 3 times in a multiplication, makes 8) 2. The Logarithm takes 2 and 8 and gives 3 (2 makes 8 when used 3 times in a multiplication) So a logarithm actually gives us the expo...
Exponents and Logarithms work well together because they "undo" each other (so long as the base "a" is the same): They are "Inverse Functions" Doing one, then the other, gets us back to where we started: It is too bad they are written so differently ... it makes things look strange. So it may help to think of ax as "up" and loga(x)as "down": Anyway...
When the base is Euler's Number e = 2.718281828459...we get: And the same idea that one can "undo" the other is still true: ln(ex) = x e(ln x)= x And here are their graphs: They are the same curve with x-axis and y-axis flipped. Which is another thing showing us they are inverse functions. Always try to use Natural Logarithms and the Natural Expone...
When the base is 10we get: 1. The Common Logarithmlog10(x), which is sometimes written as log(x) Engineers love to use it, but it is not used much in mathematics.
What if we want to change the base of a logarithm? We can use this formula: "x goes up, a goes down" 1logb aworks as a "conversion factor" from one base to any other base. Another useful property is: See how "x" and "a" swap positions? And we use the Natural Logarithm so often it is worth remembering this: Here is another example:
Exponent Formula and Rules. Exponents have certain rules which we apply in solving many problems in maths. Some of the exponent rules are given below. Zero rule: Any number with an exponent zero is equal to 1. Example: 8 0 = 1, a 0 = 1. One Rule: Any number or variable that has the exponent of 1 is equal to the number or variable itself ...
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May 23, 2017 · For an exponent of 2, we used the word “squared”, and for an exponent of 3, we use the word “cubed”. Exponents are important in math because they allow us to abbreviate something that would otherwise be really tedious to write. If we want to express in mathematics the product of x multiplied by itself 7 times, without exponents we’d ...
