If ${log}_{10} 2 = a$ and ${log}_{10} 3 = b$ , then express $log 2.25$ in terms of $a$ and $b$

2 b + 2 a

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2 b - a

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2 b - 2 a

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b - 2 a

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Solution

The correct option is C $2 b - 2 a$
Given, $x = log 2.25$
$⟹ x = log \frac{9}{4}$
$⟹ x = log 3^{2} - log 2^{2}$ (Using $log \frac{a}{b} = log a - log b)$
$⟹ x = 2 log 3 - 2 log 2$ (Using $log a^{b} = b log a$ )
$⟹ x = 2 b - 2 a$

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