Prove ${log}_{10} 30 = 1 + {log}_{10} (3)$

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Solution

${log}_{10} 30 = {log}_{10} (10 \times 3)$
We know
${log}_{10} a b = {log}_{10} a + {log}_{10} b$
${log}_{10} 10 \times 3 = {log}_{10} 10 + {log}_{10} 3 = 1 + {log}_{10} 3$
Hence proved.

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