Question

solve 3^x2:3^x=9:1 find x

Answer 1

$Heya$‼


$3^(x^2) : 3^x = 9 : 1$

$3^(x^2)$ $/ 3^x = 9 / 1$

3^x²-x $= 9$

$3^x = 9$

$3^2 = 9$


$Therefore,$$x=2$

Answer 2

HEYA !

${3}^{ {x}^{2} } : {3}^{x} = 9 : 1 \\ \\ \Rightarrow \: \: \: \frac{ {3}^{ {x}^{2} } }{ {3}^{x} } = \frac{9}{1} \\ \\ \Rightarrow \: \: \: {3}^{ {x}^{2} - x } = {3}^{2} \: \: \: \: \: \: \: \biggl\{ \: \because \frac{ {a}^{m} }{ {a}^{n} }= {a}^{m - n} \: \biggl \}$
On equating the Power of 3 , We get

${x}^{2} - x = 2 \\ \\ \Rightarrow \: \: \: {x}^{2} - x - 2 = 0 \\ \\ \Rightarrow \: \: \: {x}^{2} - 2x + x - 2 = 0 \\ \\\Rightarrow \: \: \: {x}(x - 2) + 1(x - 2) =0 \\ \\\Rightarrow \: \: \: (x - 2)(x + 1) = 0 \\ \\ \Rightarrow \: \: \:x - 2 = 0 \: \: \: \text{or} \: \: \: x + 1 = 0 \\ \\ \Rightarrow \: \: \:x = 2 \: \: \: \text{or} \: \: \: x = - 1 \\ \\ \Rightarrow \: \: \: \boxed{x = 2 \: \: \text {or} \: - 1} \: \: \: \: \: \: \textbf{Ans.}$