Answer
$-3$
Work Step by Step
$\log_{b}x=y $ is equivalent to $ b^{y}=x.\qquad (*)$
Consequently,$\qquad \log_{b}b^{x}=x.\qquad (**)$
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$\displaystyle \frac{1}{1000}=\frac{1}{10^{3}}=10^{-3}\quad $... (we applied a rule for exponents)
The common logarithm is a logarithm with base $10,\quad(\log x=\log_{10}x).$
$\displaystyle \log\frac{1}{1000}=\log_{10}10^{-3}=\quad $... apply (**)
= $-3$
