Question

Solve for x: 9^x+2-6×3^x+1 +1=0

Answer 1

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Answer 2

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${9}^{x + 2} - 6 \times {3}^{x + 1} + 1 = 0 \\ or. \: {9}^{2} \times {9}^{x} - 6 \times 3 \times {3}^{x} + 1 = 0 \\ or. \: 81 \times {3}^{2x} - 18 \times {3}^{x} + 1 = 0 \\ or. \: {(9 \times {3}^{x}) }^{2} - 2 \times (9 \times {3}^{x} ) \times 1 + {1}^{2} = 0 \\ or. \: {(9 \times {3}^{x} - 1) }^{2} = 0 \\ or. \: 9 \times {3}^{x} - 1 = 0 \\ or. \: {3}^{2} \times {3}^{x} = 1 \\ or. \: {3}^{x} = \frac{1}{ {3}^{2} } = {3}^{ - 2} \\ \\ so...x = - 2$
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