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Property 1

If log 30 3...

Question

If ${log}_{30} 3 = a, {log}_{30} 5 = b$ , then write ${log}_{30} 75$ in terms of $a$ and $b$ .

a + 2 b

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2 a + b

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a - 2 b

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2 a - b

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Solution

The correct option is B $a + 2 b$
Given that:
${log}_{30} 3 = a$ and ${log}_{30} 5 = b$
${log}_{30} 75 = {log}_{30} (25 \times 3)$
$= {log}_{30} 25 + {log}_{30} 3$
$= {log}_{30} 5^{2} + {log}_{30} 3$
$= 2 {log}_{30} 5 + {log}_{30} 3$
$= 2 b + a$
$= a + 2 b$
Hence, A is the correct option.

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