Question

Which of the following is equal to log(sq root 1000)?
1)2/3
2)-2/3
3)3/2
4)-3/2

Answer 1

To evaluate \( \log(\sqrt{1000}) \), we start by simplifying \( \sqrt{1000} \):

\[
\sqrt{1000} = \sqrt{10^3} = 10^{3/2}
\]

Now, we can apply the logarithm property \( \log(a^b) = b \cdot \log(a) \):

\[
\log(\sqrt{1000}) = \log(10^{3/2}) = \frac{3}{2} \cdot \log(10)
\]

Since \( \log(10) = 1 \):

\[
\log(\sqrt{1000}) = \frac{3}{2} \cdot 1 = \frac{3}{2}
\]

Thus, the value of \( \log(\sqrt{1000}) \) is:

\[
\frac{3}{2}
\]

Therefore, the answer is:

\[
\boxed{3/2}
\]