But I don't know their values!

Algebra Level 1

log ( a 2 b c ) + log ( b 2 a c ) + log ( c 2 a b ) = ? \large\log\left(\dfrac {{a}^{2}}{bc}\right)+\log\left(\dfrac {{b}^{2}}{ac}\right)+\log\left(\dfrac {{c}^{2}}{ab}\right) = \ ?


The answer is 0.

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3 solutions

Mehul Arora
Jun 16, 2015

log a + log b + log c = log ( a b c ) \log a+\log b+\log c= \log(abc)

log ( a 2 b c ) + log ( b 2 a c ) + log ( c 2 a b ) = log ( ( a b c ) 2 a b × b c × c a ) \log\left(\dfrac {{a}^{2}}{bc}\right)+\log\left(\dfrac {{b}^{2}}{ac}\right)+\log\left(\dfrac {{c}^{2}}{ab}\right)= \log \left( \dfrac {{(abc)}^{2}}{ab \times bc \times ca}\right)

log 1 \rightarrow \log 1

log 1 = 0 \log 1=0

Answer:- 0 0

I can't get the power while posting a solution

HARISH SADAGOPAN - 5 years, 11 months ago

Correct and I 've upvoted.

Hon Ming Rou - 5 years, 11 months ago
Sandeep Rathod
Jun 16, 2015

l o g ( a 3 a b c ) + l o g ( b 3 a b c ) + l o g ( c 3 a b c ) log(\dfrac {{a}^{3}}{abc})+log(\dfrac {{b}^{3}}{abc})+log(\dfrac {{c}^{3}}{abc})

l o g a 3 l o g a b c + l o g b 3 l o g a b c + l o g c 3 l o g a b c loga^3 - logabc + logb^3 - logabc + logc^3 - logabc

3 l o g a + 3 l o g b + 3 l o g c 3 l o g ( a b c ) 3loga + 3logb + 3logc - 3log(abc)

= 3 l o g ( a b c ) 3 l o g ( a b c ) = 0 = 3log(abc) - 3log(abc) = 0

Towhidd Towhidd
Jul 26, 2015

log((a^.b^2.c^2)/(bc.ab.ac))=log1=0

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