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We are to numerically calculate the first derivative of $\log_{10} x$ at $x = 310$ using tabular data from $x = 300$ to $x = 310$ with unit increments. --- ### Step 1: Construct the table of $\log_{10} x$ We first write 10-figure logarithms for $x = 300$ to $310$. From standard logarithm tables: $$ \log_{10} x = \log_{10}(3 \times 10^2) = 2 + \log_{10} 3 $$ We use the values: | $x$ | $\log_{10} x$ (10-fig) | | --- | ---------------------- | | 300 | 2.4771212547 | | 301 | 2.4785664950 | | 302 | 2.4800069429 | | 303 | 2.4814426283 | | 304 | 2.4828735759 | | 305 | 2.4842998393 | | 306 | 2.4857214830 | | 307 | 2.4871385568 | | ______ _________ ___ ________ _________ ______ ______.
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