Answer
$3 + \log{x}$
Work Step by Step
RECALL:
The product rule for logarithms:
$\log_a{bc} = \log_a{b} + \log_a{c}$
Use the product rule to obtain:
$\log{(1000x)}
\\= \log{(1000 \cdot x)}
\\= \log{1000} + \log{x}
\\=\log{10^3} + \log{x}$
Note that for all real numbers within its domain $\log{10^n}=n$.
This means that $\log{10^3} =3$.
Thus,
$\log{10^3} + \log{x}= 3 + \log{x}$