To solve for \( \log \sqrt{1000} \), we can first rewrite the expression. The square root can be expressed as an exponent:
\[ \sqrt{1000} = 1000^{1/2} \]
So we can rewrite the logarithm:
\[ \log \sqrt{1000} = \log(1000^{1/2}) \]
Using the logarithmic identity \( \log(a^b) = b \cdot \log(a) \):
\[ \log(1000^{1/2}) = \frac{1}{2} \log(1000) \]
Next, we need to find \( \log(1000) \). Since \( 1000 = 10^3 \):
\[ \log(1000) = \log(10^3) = 3 \]
Now substituting back, we get:
\[ \log \sqrt{1000} = \frac{1}{2} \cdot 3 = \frac{3}{2} \]
Thus, \( \log \sqrt{1000} \) is equal to \( \frac{3}{2} \).
The correct answer is:
\( \frac{3}{2} \) (3 halves)