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 )

Question

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 ) (A) 102 (B) 103 (C) 104 (D) 109

Tardigrade Admin · Accepted Answer

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 ( B 3 C 3 P 3 L 3)=9 ⇒ log ( BCPL )=3 ⇒ BCPL =1000

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

$1 0^{2}$

$1 0^{3}$

$1 0^{4}$

$1 0^{9}$

Given $2 lo g B + lo g L + lo g P = 2$ ....(1)
$2 lo g P + lo g L + lo g C = 3 \dots .. (2)$
$and 2 lo g C + lo g B + lo g L = 4$ .....(3)
$add lo g (B^{3} C^{3} P^{3} L^{3}) = 9$
$\Rightarrow lo g (BCP L) = 3 \Rightarrow BCP L = 1000$

Q. 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 )

102

103

104

109