Answer
$3+log_{10}x$
Work Step by Step
Based on the product rule of logarithms, we know that $log_{b}(MN)=log_{b}M+log_{b}N$ (for $M\gt0$ and $N\gt0$).
We know that $log(x)$ is a common logarithm with a base of 10. Therefore, $log(1000x)=log_{10}1000x=log_{10}1000+log_{10}x$.
Based on the definition of the logarithmic function, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (for $x\gt0$ and $b\gt0$, $b\ne1$).
Therefore, $log_{10}1000=3$, because $10^{3}=1000$. So, $log_{10}1000+log_{10}x=3+log_{10}x$.