A denotes the product \( x y z \) where \( x, y \) and \( z \) satisfy \[ \begin{array}{l} \log ....
0A denotes the product \( x y z \) where \( x, y \) and \( z \) satisfy
\( \mathrm{P} \)
\[
\begin{array}{l}
\log _{3} x=\log 5-\log 7 \\
\log _{5} y=\log 7-\log 3 \\
\log _{7} z=\log 3-\log 5
\end{array}
\]
\( B \) denotes the sum of square of solutions of the equation \( \log _{2}\left(\log _{2} x^{6}-3\right)-\log _{2}\left(\log _{2} x^{4}-5\right)=\log _{2} 3 \quad C \) denotes characteristic of logarithm
\[
\begin{array}{l}
\log _{2}\left(\log _{2} 3\right)-\log _{2}\left(\log _{4} 3\right)+\log _{2}\left(\log _{4} 5\right)-\log _{2}\left(\log _{6} 5\right)+ \\
\log _{2}\left(\log _{6} 7\right)-\log _{2}\left(\log _{8} 7\right)
\end{array}
\]
The value of \( \log _{2} A+\log _{2} B+\log _{2} C \) equal to
(1) 5
(2) 6
(3) 7
(4) 4
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