Terminology for exponentiation and logarithms

In summary, when discussing exponentiation and logarithms, the number being raised to a power (such as 2 in 2³ = 8) is referred to as the base, the power or exponent (3 in this case) indicates how many times the base is multiplied by itself, and the end result (8 in this case) is called the product. In logarithms, the base (2 in log 2 (8) = 3) remains the same, the number being raised to the base (8 in this case) is called the anti-logarithm, and the exponent or power (3 in this case) indicates the number of times the base must be multiplied by itself to get the anti-logarithm.
  • #1
wolf1728
Gold Member
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I am attempting to write a page concerning exponentiation and logarithms for my website www.1728.com

Basically I'd like to know the precise terminology.
In the equation 2³ = 8
we can say that "2" is the base, "3" is the exponent but what exactly is the "8" called? I have seen it referred to (no doubt incorrectly) as the power? I'm thinking the "8" could be called the answer, the result, or the product but there might be a better term.

In this equation,
log 2 (8) = 3

"2" is the base, "8" is the anti-logarithm and "3" is the logarithm.
(I'm guessing I have defined those correctly).

Any answers would be greatly appreciated and thank you.
 
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  • #2
Two to the third power is eight. The product is 8.

Log base two of eight is three. Your terms are good.
 

1. What is exponentiation?

Exponentiation is a mathematical operation that involves raising a number to a power. In other words, it is when a number is multiplied by itself a certain number of times. The number being multiplied is called the base, and the number of times it is multiplied is called the exponent.

2. What is the difference between exponentiation and logarithms?

While exponentiation involves raising a number to a power, logarithms are the inverse of this operation. In other words, logarithms tell us what power we need to raise a certain number to get a given result. They are often used to solve exponential equations.

3. How do you read and write exponential expressions?

Exponential expressions are typically written in the form of "a to the power of b", where a is the base and b is the exponent. For example, 2 to the power of 3 can be written as 2^3 or 23. When reading an exponential expression, you would say "2 raised to the power of 3" or "2 to the third power".

4. What are the rules for simplifying exponential expressions?

The rules for simplifying exponential expressions depend on the specific scenario, but some common rules include multiplying exponents with the same base, dividing exponents with the same base, and raising a power to another power. It is important to follow the correct order of operations when simplifying exponential expressions.

5. How are logarithms used in real life?

Logarithms are used in many real-life situations, such as calculating earthquake intensity, measuring the pH level of a solution, and analyzing the growth of bacteria or population over time. They are also used in finance, computer science, and other fields that involve exponential growth or decay.

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