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The definitive guide to logarithm: its concept, its applications, its algebraic rules and its expansion into complex numbers.
The logarithm is denoted "log b x" (pronounced as "the logarithm of x to base b", "the base-b logarithm of x", or most commonly "the log, base b, of x "). An equivalent and more succinct definition is that the function log b is the inverse function to the function x ↦ b x {\displaystyle x\mapsto b^{x}} .
logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b x = n, in which case one writes x = log b n. For example, 2 3 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log 2 8. In the same fashion, since 10 2 = 100, then 2 = log 10 100.
A logarithm is the inverse of the exponential function. Specifically, a logarithm is the power to which a number (the base) must be raised to produce a given number. For example, \(\log_2 64 = 6,\) because \( 2^6 = 64.\) In general, we have the following definition: \( z \) is the base-\(x\) logarithm of \(y\) if and only if \( x^z = y \). In ...
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.
Logarithms are the inverse operation of exponentiation. We can use logarithms to find the exponent to which a given base must be raised in order to produce a particular result. For example, log 2 8 = 3 , because 2 3 = 8 .
Introduction to Logarithms. In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number? Example: How many 2 s multiply together to make 8? Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2 s to get 8. So the logarithm is 3. How to Write it. We write it like this: log2(8) = 3.
