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The value of the common logarithm is undefined at 0.

Q: What is the value of logarithm of zero?

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Zero, in logs to base 10, base e, or any base.

The base b logarithm of x is a value y such that by = x

I am not quite sure what you mean with "log you"; the log is calculated for numbers. The following logarithms are undefined: For real numbers: the logarithm of zero and of negative numbers is undefined. For complex numbers: the logarithm of zero is undefined.

In the real numbers, the logarithm is only defined for positive numbers. The logarithm of zero or a negative number is undefined. (For calculators who work with complex number, only the logarithm of zero is undefined.) This follows from the definition of the logarithm, as the solution of: 10x = whatever "Whatever" is the number of which you want to calculate the logarithm. Since 10x is always positive, that means you can't find an "x" such that the power results in a negative number, or in zero. The same applies if you use a base other than 10, for example the number e = 2.718...

determination of log table value

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I suppose you mean log21 - the logarithm of 1, to the base 2. The logarithm of 1 (in any base) is zero, since x0 = 1 for any "x".

Zero, in logs to base 10, base e, or any base.

The base b logarithm of x is a value y such that by = x

I am not quite sure what you mean with "log you"; the log is calculated for numbers. The following logarithms are undefined: For real numbers: the logarithm of zero and of negative numbers is undefined. For complex numbers: the logarithm of zero is undefined.

A number for which a given logarithm stands is the result that the logarithm function yields when applied to a specific base and value. For example, in the equation log(base 2) 8 = 3, the number for which the logarithm stands is 8.

In the real numbers, the logarithm is only defined for positive numbers. The logarithm of zero or a negative number is undefined. (For calculators who work with complex number, only the logarithm of zero is undefined.) This follows from the definition of the logarithm, as the solution of: 10x = whatever "Whatever" is the number of which you want to calculate the logarithm. Since 10x is always positive, that means you can't find an "x" such that the power results in a negative number, or in zero. The same applies if you use a base other than 10, for example the number e = 2.718...

The Logarithm of a number is the converse of its logarithmic value..

determination of log table value

The actual calculations to get a logarithm are quite complicated; in most cases you are better off if you look the logarithm up in tables, or use a scientific calculator.

A logarithm can not be converted in to an exponential, as an exponential is defined for all real numbers, while a logarithm is only defined for numbers greater than zero. However, a logarithm can be related to an exponential by the fact that they are inverses of each other. e.g. if y = 2^x the x = log2y

If we assume a logarithm to the base e, then it is exactly 1.If we assume a logarithm to the base e, then it is exactly 1.If we assume a logarithm to the base e, then it is exactly 1.If we assume a logarithm to the base e, then it is exactly 1.

Yes. The logarithm of 1 is zero; the logarithm of any number less than one is negative. For example, in base 10, log(0.1) = -1, log(0.01) = -2, log(0.001) = -3, etc.