`E=(3^(log_(3)sqrt(9^(|x-2|)))+7^((1/5)log_(7)(4).3^(|x-2|)-9 ))^(7)`

Find the sum of possible real values of x for which the sixth term of (3^(log_3 sqrt(9^|x-2|))+7^(1/5 log_7 (3^(|x-2|-9))))^7 equals 567.

the value of x, for which the 6th term in the expansions of [2^(log_(2))(sqrt(9^((x-1)+7)))+(1)/(2^((1)/(5))(log)_(2)(3^(x-1)+1))]^(7) is equal to a.4 b.3 c.2 d.1

If x=4^(log_(2)(sqrt(9^(k-1)+7))) and y=(1)/(32^(log_(2)(3^(k-1)+1)^((1)/(5)))) and xy=4 then find sum of the squares of the real values of k

log_((3)/(4))log_(8)(x^(2)+7)+log_((1)/(2))log_((1)/(4))(x^(2)+7)^(-1)=-2

log_((3)/(4))log_(8)(x^(2)+7)+log_((1)/(2))log_((1)/(4))(x^(2)+7)^(-1)=-2

sqrt(log_(3)(3x^(2))log_(9)(81x))=log_(9)x^(3)

If log_(2)(3^(2x-2)+7)=2+log_(2)(3^(x-1)+1) then x=