#2015_20 Solve for \(x\)

Algebra Level 5

Find the sum of values of \(x\) for which the sixth term from beginning of the expansion of \[E={\large\large \left( { 3 }^{ \log _{ 3 }{ \sqrt { { 9 }^{ \left| x-2 \right| } } } }+{ 7 }^{ \left( \frac { 1 }{ 5 } \log _{ 7 }{ (4).{ 3 }^{ \left| x-2 \right| } } -9 \right) } \right) }^{ 7 }\] is 567 .

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