Chapter 5 - Logarithmic Functions - 5.1 Logarithms and Their Properties - Exercises and Problems for Section 5.1 - Exercises and Problems - Page 193: 12

$\frac{3}{2}$

We know that $\log_ab=c\Leftrightarrow a^c=b$ and $\ln b=c\Leftrightarrow e^c=b$. Also, $\log_a a^x=x$ and $\log_a b^x=x\log_a b$ Hence here: $\log\sqrt{1000}=\log{(10^3)^{\frac{1}{2}}}=\log{10^{\frac{3}{2}}}=\frac{3}{2}\log10=\frac{3}{2}\cdot1=\frac{3}{2}$