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The logarithmic function is not defined for zero or negative numbers.

Logarithms are the inverse of the exponential function for a positive base. Any exponent of a positive base must be positive. So the range of any exponential function is the positive real line. Consequently the domain of the the inverse function - the logarithm - is the positive real line. That is, logarithms are not defined for zero or negative numbers.

(Wait until you get to complex analysis, though!)

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Q: Why negative numbers don't have logarithim?
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