If log 12 27- a- then log 6 16-A- None of theseB- 2 3- a -3 -2C- 3 3-3D- 4 3-a-3-a

The correct option is D 43 a/3+a log_6 16=log_6 2^4=4log_6 2=4/log_2 6 =4/log_2 2+log_2 3=4/1+log_2 3 and a=log_12 27=log_12 3^3=3log_12 3 =3/log_3 12=3/log_3 ...

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Byju's Answer

Standard IX

Mathematics

Property 4

If log 12 27=...

Question

If $l o g_{12} 27 = a$ , then $l o g_{6} 16 =$

$2 \frac{3 - a}{3 + a}$

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$3 \frac{3 - a}{3 + a}$

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$4 \frac{3 - a}{3 + a}$

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None of these

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Solution

The correct option is C
$4 \frac{3 - a}{3 + a}$

$l o g_{6} 16 = l o g_{6} 2^{4} = 4 l o g_{6} 2 = \frac{4}{l o g_{2} 6}$
$= \frac{4}{l o g_{2} 2 + l o g_{2} 3} = \frac{4}{1 + l o g_{2} 3}$
and $a = l o g_{12} 27 = l o g_{12} 3^{3} = 3 l o g_{12} 3$
$= \frac{3}{l o g_{3} 12} = \frac{3}{l o g_{3} 3 + l o g_{3} 4}$
$= \frac{3}{1 + 2 l o g_{3} 2}$
$∴ a + 2 a l o g_{3} 2 = 3$
or $l o g_{3} 2 = \frac{3 - 1}{2 a}$
Hence $l o g_{2} 3 = \frac{2 a}{3 - a}$

Suggest Corrections

If log12 27=a, then log6 16=

The correct option is C 43−a3+a log6 16=log6 24=4log6 2=4log2 6 =4log2 2+log2 3=41+log2 3 and a=log12 27=log12 33=3log12 3 =3log3 12=3log3 3+log3 4 =31+2log3 2 ∴ a+2alog3 2=3 or log3 2=3−12a Hence log2 3=2a3−a

If $l o g_{12} 27 = a$ , then $l o g_{6} 16 =$