Question

What is equal to log square root 1000

Answer 1

To simplify \(\log(\sqrt{1000})\), we can use the property of logarithms that states \(\log(a^b) = b \cdot \log(a)\).

First, we rewrite the square root as a power:

\[
\sqrt{1000} = 1000^{1/2}
\]

Now apply the logarithm property:

\[
\log(\sqrt{1000}) = \log(1000^{1/2}) = \frac{1}{2} \log(1000)
\]

Next, we need to evaluate \(\log(1000)\). Since \(1000 = 10^3\), we have:

\[
\log(1000) = \log(10^3) = 3 \cdot \log(10) = 3
\]

Putting it all together:

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

Therefore, \(\log(\sqrt{1000})\) is equal to \(\frac{3}{2}\).