To solve the expression [tex]\(\log 1,000,000 - \log 100\)[/tex], we can utilize the properties of logarithms. One of the fundamental properties of logarithms is that the difference of two logarithms is equal to the logarithm of the division of their arguments. Specifically,
[tex]\[
\log a - \log b = \log \left( \frac{a}{b} \right)
\][/tex]
Applying this property to our problem,
[tex]\[
\log 1,000,000 - \log 100 = \log \left( \frac{1,000,000}{100} \right)
\][/tex]
Next, we need to simplify the fraction:
[tex]\[
\frac{1,000,000}{100} = 10,000
\][/tex]
So,
[tex]\[
\log 1,000,000 - \log 100 = \log 10,000
\][/tex]
Therefore, the simplified answer is:
[tex]\[
\log (\boxed{10,000})
\][/tex]
