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

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Question

(B) The given equation is $3^{2x} - 10 \cdot 3^x + 9 = 0$,which can be written as $(3^x)^2 - 10(3^x) + 9 = 0$. Let $a = 3^x$. Then the equation reduce

Vedclass · Accepted Answer

$0, 2$

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(B) The given equation is $3^{2x} - 10 \cdot 3^x + 9 = 0$,which can be written as $(3^x)^2 - 10(3^x) + 9 = 0$. Let $a = 3^x$. Then the equation reduces to $a^2 - 10a + 9 = 0$. Factoring the quadratic equation,we get $(a - 9)(a - 1) = 0$,which gives $a = 9$ or $a = 1$. Case $1$: If $a = 9$,then $3^x = 9 = 3^2$,so $x = 2$. Case $2$: If $a = 1$,then $3^x = 1 = 3^0$,so $x = 0$. Thus,the roots of the equation are $0$ and $2$.

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

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