Question
Select the expressions that are equivalent to: 2log(10)
Select 2 correct answers.
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(2 points)
Responses
log(20)
the log of 20
log(102)
the log of open paren 10 squared close paren
12
12
log(102)
the log of 10 halves
2
Select 2 correct answers.
Click Here for a Hint
(2 points)
Responses
log(20)
the log of 20
log(102)
the log of open paren 10 squared close paren
12
12
log(102)
the log of 10 halves
2
Answers
Answered by
GPT-4o mini
To determine which expressions are equivalent to \(2 \log(10)\), we can use properties of logarithms. Here's the breakdown:
1. **Using the logarithm property:**
\[
a \log(b) = \log(b^a)
\]
Therefore, \(2 \log(10) = \log(10^2) = \log(100)\).
Now, let's analyze each option given:
1. **log(20)** - This is not equivalent because it does not equal \(\log(100)\).
2. **the log of 20** - This is not equivalent because it does not equal \(\log(100)\).
3. **log(102)** - This equals \(\log(100)\) (the expression is the logarithm of \(10^2\)), so this is equivalent.
4. **12** - This is not equivalent because \(2 \log(10)\) will not equal 12.
5. **log(102)** - This appears to be a repeat and also equals \(\log(100)\), so this is also equivalent.
From the explanations above, the two correct answers that are equivalent to \(2 \log(10)\) are:
- **log(102)** (which is equivalent to \(\log(100)\))
- **log(102)** (the same as the previous option, reaffirmed)
So, only one unique correct answer exists, which is **log(102)**. If you are to select just two, the repetition doesn't introduce a new option, and thus, you may need clarification regarding the format of the question. If you intended to select just two unique responses, you would select the repeated response as one choice and the first occurrence as the second (since they are phrased identically).
If looking for distinctly phrased equivalents, there would only be one relevant answer here in terms of unique expression.
1. **Using the logarithm property:**
\[
a \log(b) = \log(b^a)
\]
Therefore, \(2 \log(10) = \log(10^2) = \log(100)\).
Now, let's analyze each option given:
1. **log(20)** - This is not equivalent because it does not equal \(\log(100)\).
2. **the log of 20** - This is not equivalent because it does not equal \(\log(100)\).
3. **log(102)** - This equals \(\log(100)\) (the expression is the logarithm of \(10^2\)), so this is equivalent.
4. **12** - This is not equivalent because \(2 \log(10)\) will not equal 12.
5. **log(102)** - This appears to be a repeat and also equals \(\log(100)\), so this is also equivalent.
From the explanations above, the two correct answers that are equivalent to \(2 \log(10)\) are:
- **log(102)** (which is equivalent to \(\log(100)\))
- **log(102)** (the same as the previous option, reaffirmed)
So, only one unique correct answer exists, which is **log(102)**. If you are to select just two, the repetition doesn't introduce a new option, and thus, you may need clarification regarding the format of the question. If you intended to select just two unique responses, you would select the repeated response as one choice and the first occurrence as the second (since they are phrased identically).
If looking for distinctly phrased equivalents, there would only be one relevant answer here in terms of unique expression.