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Verified answer
ᵃlog b = 1/ (ᵇlog a)1/ (x-2)' log 5 = ⁵log (x- 2)
1/(x-2)'log 5 + 2/(x-2)'log 5 + 3/ (x-2)'log 5 + ... +20/ (x-2)'log 5 =210
1. ⁵log (x-2) + 2 . ⁵log (x-2) + 3.⁵log (x-2) + ...+ 20. ⁵log(x-2) = 210
(1 + 2 + 3 + ...+20) ⁵log (x-2) = 210
210 . ⁵log (x -2) = 210
⁵log (x -2) = 1
x - 2 = 5¹
x =7