How do you solve this?

$$\\log_{10} 10000^2 - log_{10} \frac{1}{100^2} \\\\
=2*log_{10} 10000 - log_{10} 100^{-2} \\\\
=2*log_{10} 10^4 -\; -2*log_{10} 100 \\\\
=2*4*log_{10} 10 +2*log_{10} 10^2 \\\\
=8*1 +2*2*log_{10} 10 \\\\
=8 +4 \\\\
=12$$

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