Find the minimum value of
\[2 \log_{10} x - \log_x \frac{1}{100}\]for $x > 1.$
Question:
Find the minimum value of
\[2 \log_{10} x - \log_x \frac{1}{100}\]for $x > 1.$
Answer:
Let's think step by step.

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Find the minimum value of
\[2 \log_{10} x - \log_x \frac{1}{100}\]for $x > 1.$
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