Basic Idea and Rules for Logarithms

Basic Idea and Rules for Logarithms

The logarithm of any number to a given base is the power to which the base must be raised in order to equal the given number. The basic concepts of logarithms are discussed here.

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If a = N, then, logaN = x

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This is read as log N to the base a. In the equation N and a are positive numbers. Logarithms to the base 10 are known as common logarithms while logarithms to the base e are called natural logarithm. If logarithms are given without mentioning the base it is taken as common logarithm.

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Example: 64 = 4can be expressed as log464 = 3.

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Logarithms have an Integral and a Decimal part. The integral part is called as characteristic and the decimal part is called as mantissa. The number of digits a number will have will be one more than the characteristic of the logarithmic value of a number.

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Important formulae in logarithms:

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  • logaa = 1
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  • loga1 = 0
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  • loga (mxn) = logam + logan
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  • loga (m/n) = logam – logan
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  • logamp = p x logam
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  • loga m = logbm / logab
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  • a log b = b log a
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