The roots of the equation 3^{2x} - 10 cdot 3^ | vedclass

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(B) The given equation is $3^{2x} - 10 \cdot 3^x + 9 = 0$, which can be rewritten as $(3^x)^2 - 10(3^x) + 9 = 0$.Let $a = 3^x$. Substituting this into

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$0, 2$

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(B) The given equation is $3^{2x} - 10 \cdot 3^x + 9 = 0$, which can be rewritten as $(3^x)^2 - 10(3^x) + 9 = 0$.Let $a = 3^x$. Substituting this into the equation, we get the quadratic equation:$a^2 - 10a + 9 = 0$Factoring the quadratic equation:$(a - 9)(a - 1) = 0$This gives the roots $a = 9$ and $a = 1$.Now, substitute back $a = 3^x$:For $a = 9$: $3^x = 9 \Rightarrow 3^x = 3^2 \Rightarrow x = 2$.For $a = 1$: $3^x = 1 \Rightarrow 3^x = 3^0 \Rightarrow x = 0$.Thus, the roots of the equation are $x = 0$ and $x = 2$.

The roots of the equation $3^{2x} - 10 \cdot 3^x + 9 = 0$ are

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