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What is an Exponent? What is a Logarithm? A Logarithm goes the other way. It asks the question "what exponent produced this?": And answers it like this: In that example: The Exponent takes 2 and 3 and gives 8 (2, used 3 times in a multiplication, makes 8) The Logarithm takes 2 and 8 and gives 3 (2 makes 8 when used 3 times in a multiplication)
4 Αυγ 2024 · Logarithm is a mathematical function that represents the exponent to which a fixed number, known as the base, must be raised to produce a given number. In other words, it is the inverse operation of exponentiation.
The exponent says how many times to use the number in a multiplication. In this example: 2 3 = 2 × 2 × 2 = 8 (2 is used 3 times in a multiplication to get 8)
Normally, when the equation has logarithms in exponents, we usually take a suitable logarithm (it depends on the question) so that the exponents get "pulled down" and make the equation simpler. Examples
In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 10 3, the logarithm base of 1000 is 3, or log 10 (1000) = 3.
“The logarithm of a positive real number a with respect to base b, a positive real number not equal to 1 [nb 1], is the exponent by which b must be raised to yield a”. i.e. by= a ⇔logba=y. Where, “a” and “b” are two positive real numbers. y is a real number. “a” is called argument, which is inside the log.
Exponents, Roots and Logarithms. Exponents, Roots (such as square roots, cube roots etc) and Logarithms are all related! Let's start with the simple example of 3 × 3 = 9: Using Exponents we write it as: 3 2 = 9. When any of those values are missing we have a question, each with a different notation: 3 2 = ?
