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Logarithmic Function

If log r 6 ...

Question

If ${log}_{r} 6 = m$ and ${log}_{r} 3 = n$ , then what is ${log}_{r} (r / 2)$ ?

A

m - n + 1

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B

m + n - 1

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C

1 - m - n

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D

1 - m + n

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Solution

The correct option is B $1 - m + n$
${log}_{r} 6 = m, {log}_{r} 3 = n$
$l o g_{r} 6 = l o g_{r} (3 \times 2) = l o g_{r} 3 + l o g_{r} 2$
$m = n + l o g_{r} 2$
$l o g_{r} \frac{r}{2} = l o g_{r} r - l o g_{r} 2 = 1 - l o g_{r} 2 = 1 - m + n$

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