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Find the range of the function y = log3 ...

Find the range of the function `y = log_3 (5 + 4x - x^2)`.

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Here 5 + 4x -`x^2 gt rArr x^2 - 4x - 5 lt 0 rArr (x + 1)(x - 5) lt 0 rArr -1 lt x lt 5 `
But `(5 + 4x - x^2)` has the maximum value 9 at `x = 2 in [-1 , 5]
and (5 + 4x - x^2)` has the minimum value 0 at x = -1 or 5.
So the range of y is `( - infty, log_3 9 ] rArr (- infty , 2]`
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