Solve`(x-1)/(log_(3)(9-3^(x))- 3) le 1`.

1.	Solve`(x-1)/(log_(3)(9-3^(x))- 3) le 1`.
Answer» We have `(x-1)/(log_(3)(9-3^(x))-3) le 1` For this, we must have ` 9-3^(x) gt 0 or 3^(x) lt 9 or x lt 2` The given expression can be expressed as: ` ((x-1))/(log_(3)(9-3^(x))-log_(3) 27) le 1 ` ` rArr ((x-1))/(log_(3)((9-3^(x))/27))le 1` ` rArr (x-1)*log_(((9-3^(x))/27)) 3 le 1` ` rArr log_(((9-3^(x))/27))(3^(x-1)) lt 1` As ` x lt 2, 0 lt (9-3^(x))/27 lt 1` We have ` 3^(x-1) ge (9-3^(x))/27` ` rArr 9 xx 3^(x) ge 9 - 3^(x)` ` rArr 10 xx 3^(x) ge 9` ` rArr x ge log_(3) 0.9` Therefore, ` x in [log_(3) 0.9, 2)`

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