If a -log 24 12- b -log 36 24- c -log 48 36- then 1- abc is equal toA- 2 aCB- None of theseC- 2 bcD- 2 ab

The correct option is C 2 bcabc=log12/log24.log24/log36.log36/log48=log12/log48 ∴ 1+abc=log48+log12/log48=log(48.12)/log48 =log24^2/log48=2.log24/log 48=2bc ...

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Byju's Answer

Standard XII

Mathematics

Fundamental Laws of Logarithms

If a =log 24 ...

Question

If $a = l o g_{24} 12, b = l o g_{36} 24, c = l o g_{48} 36$ , then 1 + abc is equal to

2 ac

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2 bc

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2 ab

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None of these

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Solution

The correct option is B 2 bc
$a b c = \frac{l o g 12}{l o g 24} . \frac{l o g 24}{l o g 36} . \frac{l o g 36}{l o g 48} = \frac{l o g 12}{l o g 48}$
$∴ 1 + a b c = \frac{l o g 48 + l o g 12}{l o g 48} = \frac{l o g (48.12)}{l o g 48}$
$= \frac{l o g 24^{2}}{l o g 48} = 2. \frac{l o g 24}{l o g 48} = 2 b c$

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If a=log24 12,b=log36 24,c=log48 36, then 1 + abc is equal to

The correct option is B 2 bcabc=log12log24.log24log36.log36log48=log12log48 ∴ 1+abc=log48+log12log48=log(48.12)log48 =log242log48=2.log24log48=2bc

If $a = l o g_{24} 12, b = l o g_{36} 24, c = l o g_{48} 36$ , then 1 + abc is equal to