Answer
$log_{10}x-2$
Work Step by Step
Based on the quotient rule of logarithms, we know that $log_{b}(\frac{M}{N})=log_{b}M-log_{b}N$ (where $b$, $M$, and $N$ are positive real numbers and $b\ne1$).
We know that $log(x)$ is a common logarithm with an understand base of 10. Therefore, $log(\frac{x}{100})=log_{10}x-log_{10}100$.
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, $log_{10}100=2$, because $10^{2}=100$. So, $log_{10}x-log_{10}100=log_{10}x-2$.
