Before beginning to simplify the equation, don’t forget that anything inside a log cannot be negative
10^{log(3-y)} = log_{2}(9 - 2^{y}) (y>0)…………………………………(1)
3 - y = log_{2}(9 - 2^{y}) (3-y>0 =) (y<3)………………….. (2)
2^{3-y} = 9 - 2^{y}
2^{y} = t
=) 8 = 9t –t^{2}
=) t^{2}-9t+8 = 0
=) t^{2}-t-8t-8 = 0
=) t(t-1)-8(t-1) = 0
=) t = 1,8
Therefore, 2^{y} = 1 and 2^{y} = 8
=) y = 0 =) y = 3
However, from inequalities (1) and (2), y cannot take either of these value So
Correct Answer is (D)
Correct Answer: none of these
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