The sum of all possible values of x satistying 2log, (3109, (2 + log, (1 + 2lon, oltis (2) 8192 (3) 2

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( 2 log _{9}left(3 log _{4}left(2+log _{3}left(1+2 log _{2} xright)right)right)=1 ) ( Rightarrow log _{9}left(3 log _{4}left(2+log _{3}left(1+2 log _{2} xright)right)right)=frac{1}{2} ) ( Rightarrow quad 3 log _{4}left(2+log _{3}left(1+2 log _{2} xright)right)=9^{1 / 2}=3 ) ( Rightarrow quad log _{4}left(2+log _{3}left(1+2 log _{2} xright)right)=1 ) ( Rightarrow log _{3}left(1+2 log _{2} xright)=2 ) ( Rightarrow quad 1+2 log _{2} x=3^{2}=9 ) ( Rightarrow log _{2} x=8 ) ( Rightarrow quad x=2^{4}=16 ) ( Rightarrow ) Aus ofrion ( (d) )

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