Are logarithms only non-negative?

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Logarithms are typically defined for non-negative values, meaning logb x exists only when x is greater than or equal to zero. However, logarithms can be extended to all nonzero real numbers using complex number theory, which is generally not covered in high school curricula. The discussion highlights a specific example, log-3 -27, questioning its validity and suggesting that the answer should be the exponent 3. For high school students, it is advisable to focus on the standard definition where bases are non-negative. Understanding more advanced logarithmic concepts can be pursued later as mathematical knowledge expands.
mileena
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I read that logb x exists only when x >= 0

what about log-3 -27 though?

The answer should be the exponent 3, right?

Thanks!
 
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You can define the logarithm for all nonzero real numbers. But this requires complex number theory. So it's not suitable for high school.
 
micromass said:
You can define the logarithm for all nonzero real numbers. But this requires complex number theory. So it's not suitable for high school.

Thanks, I read the above though in the book Pre-Calculus for Dummies. It said all logarithms and bases were non-negative. I'm not that good on trigonometry or pre-calc.
 
mileena said:
Thanks, I read the above though in the book Pre-Calculus for Dummies. It said all logarithms and bases were non-negative. I'm not that good on trigonometry or pre-calc.

Yeah. So for now just take it as given that the bases are nonnegative. You might see the more general theory later.
 
Thank you. I will take your advice. Any less work for me is a good thing!
 
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