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A calculation like:

x = log10100

is equivalent to solving:

10x = 100

In this case, the solution is 2, so the logarithm is 2. For negative numbers, you have, for example:

x = log10-1

equivalent to:

10x = -1

But this has no solution: if you raise 10 to any power - positive, negative, or zero - you always get a positive result. Therefore, the logarithm is not defined. More specifically, it isn't defined for real numbers; in the complex number system, a solution is possible.

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