Question
Find the value of \( \log \frac{1}{2} \) rounded to the nearest thousandth. -0.300 0.301 0.302 -0.301
Ask by Hills Crawford. in the United States
Jan 17,2025
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Tutor-Verified Answer
Answer
The value of \( \log \frac{1}{2} \) rounded to the nearest thousandth is -0.301.
Solution
To find \( \log \frac{1}{2} \) (assuming the logarithm is base 10), follow these steps:
1. **Understand the Relationship**:
\[
\log \frac{1}{2} = \log 1 - \log 2
\]
Since \( \log 1 = 0 \), this simplifies to:
\[
\log \frac{1}{2} = -\log 2
\]
2. **Calculate \( \log 2 \)**:
The logarithm of 2 in base 10 is approximately:
\[
\log 2 \approx 0.3010
\]
3. **Find \( \log \frac{1}{2} \)**:
\[
\log \frac{1}{2} = -0.3010
\]
Rounded to the nearest thousandth, this is:
\[
-0.301
\]
**Answer:** -0.301
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Simplify this solution Mind Expander
To find \( \log \frac{1}{2} \), we can use the property of logarithms that states \( \log \frac{a}{b} = \log a - \log b \). Therefore: \[ \log \frac{1}{2} = \log 1 - \log 2 \] Since \( \log 1 = 0 \), this simplifies to: \[ \log \frac{1}{2} = 0 - \log 2 = -\log 2 \] Now, we need to find the value of \( \log 2 \). The approximate value of \( \log 2 \) (base 10) is about 0.301. Consequently: \[ \log \frac{1}{2} \approx -0.301 \] Rounding to the nearest thousandth gives us: \[ \log \frac{1}{2} \approx -0.301 \] Thus, the value of \( \log \frac{1}{2} \) rounded to the nearest thousandth is \( -0.301 \). The correct answer is: -0.301
