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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.
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}} .
A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction.
Here is the mathematical definition of logs. Logs Definition. A logarithm is defined using an exponent. bx = a ⇔ logb a = x. Here, "log" stands for logarithm. The right side part of the arrow is read to be "Logarithm of a to the base b is equal to x".
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, log2 64 = 6, because 2^6 = 64. 26 = 64. In general, we have the following definition: z z is the base- x x logarithm of y y if and only if x^z = y xz = y.
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 bx = 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 a function that does all this work for you. We define one type of logarithm (called “log base 2” and denoted log2) to be the solution to the problems I just asked. Log base 2 is defined so that log2c = k is the solution to the problem 2k = c for any given number c.