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The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages. It is summarized as: [2] [5] Parentheses; Exponentiation; Multiplication and division; Addition and subtraction
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.
An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part. The fractional part is known as the mantissa. [b] Thus, log tables need only show the fractional part. Tables of common logarithms ...
The better the initial approximation y is, the closer A is to 1, so its logarithm can be calculated efficiently. A can be calculated using the exponential series, which converges quickly provided y is not too large. Calculating the logarithm of larger z can be reduced to smaller values of z by writing z = a · 10 b, so that ln(z) = ln(a) + b ...
The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a [4] (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, leads to the term "natural".
Commutativity and associativity are laws governing the order in which some arithmetic operations can be carried out. An operation is commutative if the order of the arguments can be changed without affecting the results. This is the case for addition, for instance, + is the same as +. Associativity is a rule that affects the order in which a ...
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