Find the minimum value of
\[2 \log_{10} x - \log_x \frac{1}{100}\]for $x > 1.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the minimum value of
\[2 \log_{10} x - \log_x \frac{1}{100}\]for $x > 1.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
Find the minimum value of
\[2 \log_{10} x - \log_x \frac{1}{100}\]for $x > 1.$
train