What is \log_{10} 31.25 equal to?

Explanation

We can write 31.25 = \frac{3125}{100} = \frac{5^5}{10^2}. Applying logarithms, \log_{10} \left(\frac{5^5}{100}\right) = 5 \log_{10} 5 - 2. Using \log_{10} 5 = 1 - \log_{10} 2, this becomes 5(1 - \log_{10} 2) - 2 = 3 - 5 \log_{10} 2.

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