Answer
$\log{x} - 2$
Work Step by Step
RECALL:
(i) $\log_b{\frac{M}{N}}=\log_b{M} - \log_b{N}$ (Quotient Rule).
(ii) $\log{x}=\log_{10}{x}.$
(iii) $\log_b{b^x}=x.$
Use the quotient rule with $M=x$ and $N=100$ to obtain
$\log{x} - \log{100}
\\=\log{x} - \log{10^2}.$
Simplify the second term by using rules (ii) and (iii) above to obtain
$\log{x} -\log_{10}{10^2}
\\=\log{x} - 2.$
