Solve $3^{2 x} + {10.3}^{x} - 9 = 0$

0, 2

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2, 2

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- 2, 2

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3, 2

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Solution

The correct option is A $0, 2$
Consider the given equation,

$3^{2 x} + {10.3}^{x} - 9 = 0$

Let , $y = 3^{x}$

Now ,

$y^{2} - 10 y + 9 = 0$

$y^{2} - 9 y - y + 9 = 0$

$y (y - 9) - 1 (y - 9) = 0$

$(y - 9) (y - 1) = 0$

When,

$x - 9 = 0$

$x = 9$

Now ,

$9 = 3^{x}$

$3^{2} = 3^{x}$

$x = 2$

When,

$y - 1 = 0$

$y = 1$

$3^{x} = 1$

$3^{x} = 3^{0}$

$x = 0$

$x = 0$ , $x = 2$

This is the answer .

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