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Question
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
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Solution
Given equation `9^(x + 2) -6.3^(x + 1) + 1 = 0`
⇒ 9x.92 - 6.3x.31 + 1 = 0
⇒ 81.(32)x - 18.3x + 1 = 0
⇒ 81.32x - 18.3x + 1 = 0
Putting 3x = y, then it becomes 81y2 - 18y + 1 = 0
⇒ 81y2 - 9y - 9y + 1 = 0
⇒ 9y(9y - 1) -1(9y - 1) = 0
⇒ (9y - 1) (9y - 1) = 0
⇒ 9y = 1
⇒ y = `(1)/(9)`
But 3x = `(1)/(9) = (1)/(3^2) = 3^-2`
∴ x = -2
Hence, the required root is -2.
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