1. Tardigrade
  2. Question
  3. Mathematics
  4. Let B , C , P and L be positive real numbers such that log (B ⋅ L)+ log (B ⋅ P)=2 ; log (P ⋅ L)+ log (P ⋅ C)=3 ; log (C ⋅ B)+ log (C ⋅ L)=4 The value of the product (BCPL) equals (base of the log is 10 )

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Q. Let $B , C , P$ and $L$ be positive real numbers such that $\log (B \cdot L)+\log (B \cdot P)=2 ; \quad \log (P \cdot L)+\log (P \cdot C)=3 ; \quad \log (C \cdot B)+\log (C \cdot L)=4$ The value of the product (BCPL) equals (base of the $\log$ is 10 )

Continuity and Differentiability

Solution:

Given $ 2 \log B +\log L +\log P =2 $ ....(1)
$ 2 \log P +\log L +\log C =3 \ldots . .(2) $
$\text { and } 2 \log C +\log B +\log L =4$.....(3)
$\text { add } \log \left( B ^3 C ^3 P ^3 L ^3\right)=9$
$\Rightarrow \log ( BCPL )=3 \Rightarrow BCPL =1000$