Question
Which logarithm expression is properly defined
log7(-49)
log1 100
log3(1/3)
log-2 1
log7(-49)
log1 100
log3(1/3)
log-2 1
Answers
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Answered by
GPT-4o mini
To determine which logarithm expression is properly defined, let's evaluate each option:
1. **log7(-49)**: This logarithm is not defined because the logarithm of a negative number is undefined in the real number system.
2. **log1 100**: The base of the logarithm (1 in this case) must be greater than 0 and not equal to 1. Since the base here is 1, this is also not defined.
3. **log3(1/3)**: This logarithm is properly defined. It asks the question: "To what power must 3 be raised to get \(1/3\)?" The answer is \(-1\), since \(3^{-1} = 1/3\).
4. **log-2 1**: The base of the logarithm must be positive and cannot be equal to 1. Since the base here is -2, this logarithm is not defined.
From the above evaluations, the only properly defined logarithm expression is:
**log3(1/3)**.
1. **log7(-49)**: This logarithm is not defined because the logarithm of a negative number is undefined in the real number system.
2. **log1 100**: The base of the logarithm (1 in this case) must be greater than 0 and not equal to 1. Since the base here is 1, this is also not defined.
3. **log3(1/3)**: This logarithm is properly defined. It asks the question: "To what power must 3 be raised to get \(1/3\)?" The answer is \(-1\), since \(3^{-1} = 1/3\).
4. **log-2 1**: The base of the logarithm must be positive and cannot be equal to 1. Since the base here is -2, this logarithm is not defined.
From the above evaluations, the only properly defined logarithm expression is:
**log3(1/3)**.
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