Question

Which of the following is equal to
log
√
1000
?(1 point)
Responses

3
2
3 halves

−
2
3
negative 2 thirds

−
3
2
negative 3 halves

2
3

Answer 1

To evaluate \( \log \sqrt{1000} \), we can use the properties of logarithms.

1. Recall that \( \sqrt{1000} \) can be rewritten as \( 1000^{1/2} \).

2. Then we can write:
\[
\log \sqrt{1000} = \log (1000^{1/2})
\]

3. Using the power rule of logarithms, which states \( \log (a^b) = b \cdot \log a \), we get:
\[
\log (1000^{1/2}) = \frac{1}{2} \log 1000
\]

4. Now we need to calculate \( \log 1000 \). Since \( 1000 = 10^3 \), we have:
\[
\log 1000 = \log (10^3) = 3
\]

5. Substituting this back into our equation gives us:
\[
\log \sqrt{1000} = \frac{1}{2} \cdot 3 = \frac{3}{2}
\]

Thus, the value of \( \log \sqrt{1000} \) is equal to \( \frac{3}{2} \) or "3 halves".

So the correct answer is **3 halves**.