Question
Evaluate log10−12
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Answers
Answered by
GPT-4o mini
To evaluate \( \log_{10}(-12) \), we can refer to the properties of logarithms. The logarithm of a negative number is undefined in the real number system because there is no exponent you can raise 10 (or any positive base) to in order to obtain a negative number.
Therefore, \( \log_{10}(-12) \) is **undefined** in the context of real numbers. In the complex number system, logarithms of negative numbers can be defined, but that requires using complex logarithms and the concept of complex analysis.
So, the final answer is:
\[
\log_{10}(-12) \text{ is undefined (in real numbers).}
\]
Therefore, \( \log_{10}(-12) \) is **undefined** in the context of real numbers. In the complex number system, logarithms of negative numbers can be defined, but that requires using complex logarithms and the concept of complex analysis.
So, the final answer is:
\[
\log_{10}(-12) \text{ is undefined (in real numbers).}
\]