Let us assume that \(35.1258 \times 0.4111 \) equals to \( 14.4402\) up to 6 significant figures.

For some constant \(a\), if \( 0.0351258 \times 4111 \times a \) equals to \( 0.144402 \) up to 6 significant figures, find the value of \(\log_{10} a \).

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