Answer
$\log{x}-3$
Work Step by Step
RECALL:
The quotient rule for logarithms states:
$\log{\left(\frac{b}{c}\right)} = \log{b} - \log{c}$
Use the quotient rule to obtain:
$\log{\left(\frac{x}{1000}\right)}
\\= \log{x} - \log{1000}
\\=\log{x} - \log{(10^3})$
Note that for all real numbers within its domain, $\log{(10^n)}=n$.
This means that $\log{(10^3)} =3$.
Thus,
$\log{x} -\log{(10^3)}= \log{x}-3$
