Simplify \(1\times {10}^{-3}\) to \({10}^{-3}\).
\[Log\times \frac{0.1}{{({10}^{-3})}^{2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[Log\times \frac{0.1}{{(\frac{1}{{10}^{3}})}^{2}}\]
Simplify \({10}^{3}\) to \(1000\).
\[Log\times \frac{0.1}{{(\frac{1}{1000})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[Log\times \frac{0.1}{\frac{1}{{1000}^{2}}}\]
Simplify \({1000}^{2}\) to \(1000000\).
\[Log\times \frac{0.1}{\frac{1}{1000000}}\]
Invert and multiply.
\[Log\times 0.1\times 1000000\]
Simplify.
\[100000gLo\]
Regroup terms.
\[100000Log\]
100000*Lo*g
