If ${log}_{10} 4 = 0.6021$ and ${log}_{10} 5 = 0.6990$ , then find the value of ${log}_{10} 1600$ .

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Solution

${log}_{10} 1600 = {log}_{10} (64 \times 25) = {log}_{10} (4^{3} \times 5^{2})$
$= {log}_{10} 4^{3} + {log}_{10} 5^{2}$
$= 3 {log}_{10} 4 + 2 {log}_{10} 5$
$= 3 (0.6021) + 2 (0.6990)$
$= 1.8063 + 1.3980$
${log}_{10} 1600 = 3.2043$

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