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Conversion of Numbers Using Logarithms

If log102 =...

Question

If ${log}_{10} 2 = a$ and ${log}_{10} 3 = b$ , then $log 12$ can be expressed as

A

2 a - b

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B

2 a + 2 b

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C

a - b

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D

2 a + b

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Solution

The correct option is D $2 a + b$
${log}_{10} 2 = a {log}_{10} 3 = b log 12 = log (2 \times 2 \times 3) = log (2^{2} \times 3) = 2 log 2 + log 3 = 2 a + b$

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