Find the value of x for which the sixth ...

Find the value of x for which the sixth term of : `(sqrt(2^(log(10-3^x)))+ root (5)(2^((x-2)log 3)))^n` is equal to 21, if it is known that the binomial coefficient of the 2nd, 3rd and 4th term in the expansion represent respectively the 1st, 3rd and 5th term of an A.P. (the symbol log stands for logarithm to the base 10).

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