Solving the equation 3

^{2x}- 10(3^{x}) + 9 = 0. What are the two solutions?Solving the equation 3^{2x} - 10(3^{x}) + 9 = 0. What are the two solutions?

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Olney, MD

3^{2x} - 10(3^{x}) + 9 = 0

(3^{x})^{2} - 10(3^{x}) + 9 = 0 [3^{2x} = (3^{x})^{2}]

Let u = 3^{x}

u^{2} - 10u + 9 = 0

Factors to:

(u-9)(u-1) = 0

u = 9, 1

u = 3^{x} = 9, so** x = 2 ** [3^{2}=9]

u = 3^{x} = 1, so **x = 0 **
[3^{0}=1]

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