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Logarithms

If log 102=...

Question

If ${log}_{10} 2 = 0.3010$ & ${log}_{10} 3 = 0.4771$ , then the value of ${log}_{10} (2.25)$ is

A

0.3522

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B

0.3532

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C

0.3265

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D

0.3256

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Solution

The correct option is A $0.3522$
${log}_{10} 2.25$
$= {log}_{10} \frac{9}{4} = 2 {log}_{10} \frac{3}{2}$
$= 2 (log 3 - log 2) = 2 (0.4771 - 0.3060) = 2 (0.1761) = 0.3522$

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